FAST Prime Factorization (5-digit number)

If this helps you, please click LIKE and help me too. Thanks!
You can use short division repeatedly to quickly find all the prime factors of a LARGE number.
2 speed keys to fast prime factorization:
• knowing your tables
• being able to choose suitable prime divisors (rules of divisibility)
This demo takes you through my thinking through the prime factorization of 76,230.
How to choose prime divisors (rules of divisibility) 2, 3, 5 and 7 are shown and described.
Answer shown by simple factor listing (axbxb etc),
and using exponential notation.

[@user-re6vl1ld1y]

I am a math teacher from Egypt ....and i really enjoyed your lesson ...you are a gifted teacher...thanks

[@LetsDoMath]

Thank you very much, Mohamad. That is very kind. It means a lot to me.

[@user-re6vl1ld1y]

you are welcome mis LadyDMcollector ....i just said the truth ...just keep creating these amazing videos

[@LetsDoMath]

Next one... Understanding Roman Numerals. Coming soon. Please watch for it Mohamad.

[@user-re6vl1ld1y]

I will b wait for that .... 👍👍 thanks Maam

[@oliverbeck6839]

a little worrying that a math teacher has to watch this video LMAO i guess egypt has lower standards x)

[@a.pal_yt2018]

Thanks very much! Tomorrow is my maths exam and I'm preparing best as I can. It'll help me, I'm in junior college, still watching this. Helpful video. 🙂

[@LetsDoMath]

Best of luck! The best you can do now is go over your notes, read through the process on any math you found tricky and refamiliarise yourself with it, doing a couple of examples (probably from some online site like math-aids.com where you can check your answers). Prime factorization is kind of a memory-muscle thing. Once you've done enough of it, you just remember it. I doubt they'll give you numbers big enough to force the use of this method, but I like to be prepared for all eventualities. Usually the factor tree is good enough. To be honest what I do now with a big number is combine the two. So I'll divide until I can spot a value from my tables knowledge, then flick into factor-tree mode and finish it in a couple of seconds. But always circle your primes so you don't accidentally miss any. All the best for your exam tomorrow, I hope it's a walk in the park for you. 😃🤗😎🤩👍💕

[@vslingam000]

It is using your explanation of the Rules of Divisibility that really did the trick. Thank you so much.

[@LetsDoMath]

Glad to help. 😃🤗

[@JMartinez69261]

For super fast factoring I first notice the 0. So I am taking a 2 and 5 all at once. I also look to grab another 2 or 3 at the same time. In her case I'd first divide by 30 and repeat. Also, checking divisibility by three does not require you have the total. Just skip over the 3,6, and 9 digits. In her example just add 7 and 2. As a matter of fact, while you are doing 3 do 9 at the same time. In that case skip any 9s, but you do need to see that 6 and 3 are nine, and you can group 7 and 2 to be a nine. My first division might have been a 90 in her example.

[@LetsDoMath]

Oooh, Jim! You're a math-BEAST! I love it! I can spot them, like you, but I definitely feel more comfortable going one at a time, even though I can see what's coming next. Maybe I just need to do a bunch more (as if I have time for that!! lol). I like to get to the point where I can spot a big one, then jump into a factor tree and finish it with a speedy flourish.

[@vamsikrishna6563]

You deserve 1 Million subscribers

[@LetsDoMath]

THANKS. That's a lovely thought. Have a fabulous day, stay safe and well.

[@patriciacampos5704]

You made it so easy to understand. Thank you so much!! I appreciate people like you who take the time to help those who want to learn. Thanks again! :)

[@LetsDoMath]

Thanks. I appreciate notes like this, from people who want to learn. I’m trying to help and it makes me happy that I have helped you. 😃🤗😎💕👍

[@Chroniclesofdora]

Hey....! LOVE ❣️ from🤩.....India , KERALA Thanks a lot for this trick never forget your video 🥺🥺

[@LetsDoMath]

Hi there! Love from Canada!! 💕 Glad you like this strategy. 🤗😃

[@DynooMitoo]

THNKS SO MUCH TOMORROW IS MY EXAM AND IT ALWAYS TOOK ME SO MUCH TIME TO FIND CUBE ROOTS BUT NOW I CAN FIND IT EASILY

[@sergejpetkovic2414]

Help you SO MUCH I tried and tried and could not learn this, I am in sixth grade,we are not learning this but I just wanted to calculate third roots☺

[@LetsDoMath]

Please do yourself a favour and just focus on nailing the prime factorization of a given number. You can get to cube roots at some point in the future.

[@StomachAcid]

That's awesome that you could do this! I'm in 7th grade and this video was really really helpful for me too

[@LetsDoMath]

Glad to help! 😎🤗

[@vijivinu4214]

Me to

[@Hoppitot]

bruh L is a genious I'm in university and don't know this XD

[@rSAMURAI_]

amazing explanation, Your way of talking and teaching is really good, thanks alot

[@LetsDoMath]

Thank you very much. You can see, using this method, there's nothing to be scared of, if your teacher gives you a really big number.

[@qaderquadri1]

Ur way of explaining is very nice i could explain it to my son very nicely thank u please keep making more of such videos n also make a video on data handling stay blessed

[@RupertBruce]

Excellent explanation with no dreary introduction or silly music.

[@LetsDoMath]

Thanks Rupert. I want to make every second count. Glad you rate it. 😎😃

[@UshaRani-ti6hk]

I am from Germany your classes helped so much for my daughter jisio

[@LetsDoMath]

Thank you. I am so pleased to help. 🤗🥰

[@notspaso6644]

It was easy only because you choose a number with those prime factors, if a number, say 'x', is composite then it has at least one prime less then the square root of x, (x^1/2), so take for example 30623 if you tried to factor it, even supposing you knew divisibility test for a lot of primes like 13, 17, 19, 23... (i guess no one would learn divisibility for primes bigger than these) you would still not be able to factor the example that i gave you because you had to check all the primes up to 174, (in fact 30623 is actually 113*271) It's okay that you show a way to factor MOST 5 digit numbers, but a side note on why this doesn't always work would've made the video more useful for the viewers

[@LetsDoMath]

This is an interesting comment. The process worked easily because I created the number by multiplying up my chosen primes, then I just chose my logical order to extract the primes. I think this is a reasonable thing to do, since at up to grade 8, I don't expect ANY teacher would give an example like the one you came up with. Please remember that this channel is about giving students the power and confidence to do the math, not about showing them that it could possibly be super-tricky and you may find it stumps you completely. They've had enough of that experience already, by the time they find me. The hardest school example I'd expect to be given would end up delivering a prime such as 41, or 59 (a prime under 100 in any case) at the end of the division sequence, and students would be expected to spot that as a prime, not know its divisibility rules. I only ever show what I feel is needed in a video to get students revved up to have a crack - none of my videos is about running to a certain time (my kids tell me 10 minutes is the magic KZbin earning length). Only what you need, and enough examples so I think students will get the approach and be ready to roll. Thanks for sending me your note. :o)

[@notspaso6644]

LadyDMcollector Thanks for clarifying, I tought I could "add" some insight for the ones who have no trouble on this topic, I didn't want to show how It can get tricky, rather I think too many students just learn to do things mechanically without understanding the essence of It... Anyway, thanks for the kind response! :)

[@LetsDoMath]

Awesome reply. Loved it! Have a wonderful day. :o)

[@jeffw1267]

I answered this before I saw your comment, but I said basically the same thing. I don't think you'd ever be asked to factor a number like 30623 on a test, but it's good to know how. And it's a MASSIVE amount of work if you're doing it mentally. If you are allowed to use a calculator, it would be very easy because you could divide 30623 by 3, 7, 11, 13, and so on and simply see if the answer comes out even. You would have to have the primes memorized up to 173 in this case. If you didn't, then you'd have to divide by EVERY number ending in 1, 3, 7, or 9 (because those COULD be primes), and it would take longer.

[@notspaso6644]

@@jeffw1267 yeah for sure no teacher would "trick" you with such question, but nevertheless no matter how I try I cannot single-handedly improve my school, thus I'd like other resources (such as internet) to provide something more for who Is willing to learn "one step further" my comment was just aimed at giving intuition towards the concept that prime numbers are like "Building blocks" for Natural numbers, (Check "fundemental theorem of arithmetic" for more details), primes are beautyful just like maths in general, there's no such thing as ugly maths but it's teachers fault whom just want you to know that "A Is true", or "Given this follow this pattern of steps and you complete the exercise", good job now you can exit school with your sufficiently high grade having your brain programmed to be able to do those things (until you don't forget them of course), they spend more time forcing the students to learn something than they do motivating the students to study in the first place, Sorry for the very long comment, didn't want to be missunderstood... Greetings ^_^

[@roseclouds6776]

thank you so much! im in eight grad and I never understood this until now, I scored above 90 in my square and square roots test because of this video! thank you :)

[@LetsDoMath]

Well done! That’s amazing! A+ grade... way to GO! 🤩🤩🤩🤗😎💕

[@gireeshthakkar3415]

O me too I am learning this for only this chapter and in 8

[@Notbeingahuman]

Mee too

[@lusandalores8618]

Omg, I’m gonna be tested on this soon, thank you! This helps so much! 😃

[@deactivated6046]

An easier way to determine whether a number is divisible my 7: If the last two digits of the number are in the 7 times table, it is divisible by seven.

[@LetsDoMath]

I love the idea, but I don't think this is reliable though. I tried 456/7 (56/7=8)... Calc answer = 65.14285714. I am sorry. I wish it was right. It does work sometimes, but not always. To be really honest, the divisibility rule for 7 is so time consuming, it's actually quicker for me to just scribble a division and check. I love how you thought about it and sent me a note. Thank you so much for that. :0)

[@deactivated6046]

Oh, If i was one of those 'stealing credit proud rude girls' i would say i thought of it. But sadly, i learnt it at school. Its in our textbooks, too. I think its because i study the CBSE syllabus. but thanks for the quick reply.. i thought i wouldnt get one for like, a few months. Glad to see you're still active!

[@LetsDoMath]

I am always working on something. On the replies front...YT is set up to send an alert when someone sends me a note. And I always respond, unless it's a rude one, and those I just chuck, because who needs that sort of negativity? The thing is, it has happened a few times that it didn't alert me, and then I only spot the note if I happen to check through a film's comments. Then I feel terrible because I am late answering. So if anyone sends me a note and you don't get some kind of response, please feel free to send me another one. I don't ignore anyone. Have a lovely day. Hope the math goes well. I am heading off to take a grade 7 math class now.

[@herambsharma7408]

135 is not divisible by 7

[@gaurisaini7009]

Very helpful i have to do prime factorisation for finding square roots for very large numbers it was very helpful for me Thanks 👍👍🤗🤗

[@LetsDoMath]

Great! Glad to help 😎😉🤗💕

[@unknownfacts5986]

I am from India, I like your video.

[@LetsDoMath]

Thanks very much! 😎😃🤩💕

[@almaskhanum2574]

Best maths teacher

[@jeffw1267]

ACTUALLY.... with a trailing zero, you can immediately divide by 2 AND 5 because 2x5 = 10. So you then have 7623 x 2 x 5. 7623 could be a prime number since it ends in 1, 3, 7, or 9. By summing the digits, you get 18, which reduces to 9, which is a multiple of 3. So I KNOW that the number is divisible by 3 and once I get two factors, I can calculate the rest of the factors (if any) from that. I won't need to mess with the large number 76,230 anymore. 3 goes into 7623: 2541 times. You would again use trial division and divide 2541/3. That equals 847. The factors are now 2, 3^2, and 5. 847 is divisible by 3, and so on. The ladder method is useful, but this number was 76,230 was purposely chosen because it has a lot of small factors. What do you do if you have a number like 5039 (which happens to be prime)? You'll have to divide by 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and 67 and see if there is a remainder at each step. 71^2 = 5041, which is larger than 5039, so we don't have to test it. Even if you have the prime numbers memorized up to 100, and all the squares memorized up to 100^2, which I do, it's a massive amount of work. I do it mentally but I suppose if you have a calculator to punch, even if you have nothing memorized, it would be simpler in the end.

[@kriptik_kid]

That looks lik ur jobless

[@rekhaprajapati134]

I like this teacher

[@LetsDoMath]

Thanks! That’s nice. It sounds like you are a student who wants to learn - I like you too! 😃🤗😎👍💕

[@hanisirimuppidi6291]

IT SO HELP FULL THANK YOU SO MUCH

[@LetsDoMath]

My pleasure!

[@user-xl6yx9tv4y]

Really i appreciate u do more videos let it help everyone🎉❤

[@THEGRACESISTERSs]

Thanks a billion times.

[@LetsDoMath]

You’re very welcome. You can speed this method up even more... when you get to a number you know in your tables, you can switch to factor tree and finish it in seconds! There’s an example of me doing this in one of the vids Finding all the Factors of a Number Using Prime Factorization. 🤗😃😎😉💕

[@THEGRACESISTERSs]

OK thank you I will and can pls pls pls subscribe to Grace sisters

[@MoonlitexRose]

Thank you so much I'm in grade 6 it was really hard but when I watched your video it was really helpful.

[@LetsDoMath]

EXCELLENT! Now in this video, I'm using short division all the way down to 1. But in fact... you can go more swiftly, IF you want. Let's say you get a big number and you've whittled it down to 144. There's no reason to keep using the division method if you don't want. You know 144 is from 12x12, so you could just flick into factor tree mode if you want... and each 12 is from 3x4, and each 4 is from 2x2! Just make sure you DO circle all those primes at the end, and make sure you collect them ALL for your final statement. If you switch, once you hit a number whose factors you know, you can complete the prime factorization in seconds! Now I hope you do something REALLY cool with this knowledge and totally ACE ANY number your teacher gives you for prime factorization using this little flourish to finish off. How slick is THAT!? I'd LOVE to see your teacher's face, when they see your understanding demonstrated on the page like that!!

[@gwblack6607]

Thanks LOVE FROM INDIA 🇮🇳❤️

[@LetsDoMath]

Right back at you!! 😃🤗💕

[@tayeebullashariff9256]

Ok You post in 5 year s back but I sawed in 2021great😂😂

[@LetsDoMath]

Glad you found this! Good math technique doesn’t go out of date. 😃😉😎🤗

[@gungun4676]

Oh God I just loved it THANKS it's gonna save my 20 minutes which I used to put in my whole exercise whose actual time taking is 5 minutes!! Great !!!! I'VE SUBSCRIBED YOUR CHANNEL ONLY AT THE BASES OF THIS VIDEO HOPEFULLY I THINK IT'S GONNA BE USEFUL FOR SURE AND ONCE AGAIN THANK U SO MUCH😊

[@LetsDoMath]

Hi there. Glad this vid helped you. Once you've got your head around this, you can speed up even more! When you hit a quotient that you know from you tables knowledge, you can flick into 'factor tree mode'. For example if I got an answer of 96, I know that's the product of 8x12, so instead of writing out another division - and now those are both compound numbers, not prime, now I switch to the tree and show 8 and 12. 8 is from 2 x4, 4 is from 2x2, and I circle those 3 twos. And on the 12 side, I can say 12 is from 2x6, 6 is from 2x3. Here I circle both 2s and a 3. And I can do all that in seconds, as can you. Much faster than continuing to divide by 2 a bunch of times. Cool!

[@gungun4676]

@@LetsDoMath WOW Thank you so much!!! You are a Genius 😃 Now I understood 👍👏

[@LetsDoMath]

Glad to help. You are going to ROCK this stuff in class, homework AND tests!

[@salehsvarioustips8541]

Thank you so much madam from the deep of my heart

[@LetsDoMath]

My pleasure! So glad to help. 😃🤗😎👍💕🇬🇧

[@jaypatel8725]

One more easy trick If you see zeros then cut the number of zeros and add the 2^n*5^n in it's factor. See the below example to understand for ex:- 12500 then two factors will be (2^2)*(5*2) { 2 because there are two zeros} then it becomes 125 which is 5^3 . So all factors will be 2^2 * 5^5

[@LetsDoMath]

You’re totally on the right lines. If you see a zero at the end, you know 2 and 5 are factors. However it’s always safest with a big number like 12,500 to actually go through the process. When you do the division and explore the number like I’m showing, you discover the prime factorization is 2x2x5x5x5x5x5. 🤗😃🤩💕

[@frankdiaries]

Never thought i'd ever use 7 divisiblility test ever in my life.

[@LetsDoMath]

You could just guess and check, but where’s the fun in that?

[@firegamer6376]

Never knew how to do this method...always did by multiplying and checking... thanku so much

[@firegamer6376]

Cause I started cube roots

[@LetsDoMath]

This is going to make a big difference to you then! Great! 😃🤗😎🤩

[@firegamer6376]

@@LetsDoMath 😊

[@davidxu6289]

Thx so much, I'm in this program called kumon and their not very good at explaining. This is very helpful

[@LetsDoMath]

Hi David, I believe on the Kumon program, they don't explain and this is a policy. The student has to get it by reading the texts and just slogging through the work. I am very glad to be able to explain in a way that makes sense and gives you the boost you need. Thanks for your note.

[@ramaswamyramu3900]

It really amazing ☺️☺️☺️☺️☺️ Before seeing this l get mentle by doing prime factorization now on work l can do this easily 😆😆😆😆😆😆😆😆😆😆😆

[@LetsDoMath]

AWESOME! Rock that math! I LOVE your comment 💕😃🤗🤩🥰😎

[@ramaswamyramu3900]

Sure l will rock maths

[@ramaswamyramu3900]

And also thank yöü for your help which you do💜💜💜

[@LetsDoMath]

It's a great pleasure!

[@dikshasahai3572]

Thanks a lot for the trick you gave me👍👍👍👍👍👍

[@LetsDoMath]

My pleasure. Glad to help. :o)

[@neda8515]

I don't know what are the rules of divisibility for smaller primes. Mam ur explaination was just perfect but can u just help me with this

[@LetsDoMath]

I have a set of films on divisibility rules which will help. They were designed to open the door to this understanding to grade 4 kids though, so they might seem a bit 'kiddy'. I think you are going to find that for the prime factorization you will do in school, your numbers will break down by 2, 3, 5, 7 and 11. You attack your number through the most obvious divisor at every step of the way, like you saw me do: even number? Use 2. Ends in 5 or 0? Use 5. Can't spot a divisor? Try rule for 3. Quite quickly, as you see, you get to the point where you recognize the dividend in your tables knowledge, then you're good to finish. When 7 is needed there's a decent chance you can use your tables knowledge. The rule for 7 is messy. Look at your number in chunks of multiples of 7 to discover if 7 is a divisor. I have seen grade 6 kids get work that finished on a larger prime (43). I don't think any teacher will give you a problem that features repeated use of one like this though. Did you watch my film Finding Prime Numbers? Doing the sieve of Eratosthenes is a great idea, so you can understand what the primes up to 100 are. Very useful so you are not stuck wondering when you get down to a 2-digit prime at the end. I hope this helps you tons.

[@knowligence5637]

What a great video😀

[@LetsDoMath]

Thanks very much. :o)

[@karempudivenkataratham1063]

Madam super your explanation is very understanding hatsaf mam

[@allenjoseph7247]

thanks so much it's very fast to find factors👍👍👍

[@LetsDoMath]

Isn't it? I love this method! Takes up less space than a factor tree too.

[@salmarauf4882]

Wow thank u soooooooooo much for helping me understand this.

[@LetsDoMath]

Fantastic stuff! And if you like, you could go even faster!!! Here's how... Use the division strategy you learned here till you get a division answer (quotient) whose factors you know. For example let's say you end up with an answer to your division problem as 84. That's fabulous, because from your tables knowledge, you know you get 84 from 7 x 12. So the sprint-cut here is to jump out of division and into factor tree mode, right where you are on the page. Show that 84 as being from 7 x12, and 12 is from 2x6, 6 is from 2x3. Circle ALL the primes, just as every other prime factorization you've done. List them off in ascending order, or even better, using exponent notation, and you just aced it in double-quick time! NICE!!!

[@salmarauf4882]

@@LetsDoMath thank u soo much😊

[@LetsDoMath]

@@salmarauf4882 it’s a pleasure to help 😃🤗

[@itspriyanka4485]

Hii ma'am I am from India I really enjoyed your video and understand easily of😇😇🙏

[@LetsDoMath]

Hi Laxmi, Thanks for your note. I'm so glad it was easy to understand. It's good to be able to handle anything a teacher or exam can throw at you. It will give you lots of confidence, and that's ALWAYS a great thing. Good for you! 😃🥰🤩

[@itspriyanka4485]

@@LetsDoMath I am also glad because this one gets easy for me😇😇

[@frankdiaries]

I can see now why divisible method of composite numbers is pretty useful at larger numbers.

[@firlim]

Thank you Mrs @LadyDMcollector for this video, is there any video explaining all the rules of divisibility for smaller primes, thanks a lot for your efforts and keep this up!

[@LetsDoMath]

Hi there! You're welcome. I love this method for prime factorization - it'll whittle down to size the big numbers your teachers might throw at you without you struggling with a factor tree. On my channel, I do have videos for rules of divisibility of 2 , 3 and 5. I didn't make a video for 7, but you saw me refer to the rule for 7 in this film. Being able to spot whether 2, 3 and 5 are factors just by looking at them is an essential math skill. Generally, the numbers you'll get in school will be divisible by smaller primes (2,3,5,7,11). I ALWAYS go for the values I can spot instantly, and that means using smaller primes. 2 is very often a repeated prime, and 3. When you carve into a 3-digit+ number, then you might start to see numbers you know from your tables, like 121 which is from 11x11, both prime. Here are the links to my rules of divisibility films if you want to look at those: Rule for 2 (kzbin.info?o=U&video_id=kgAk6f1zenY&feature=vm) Rule for 3 kzbin.info?o=U&video_id=xdunx3IbkeI&feature=vm Rule for 5 kzbin.info?o=U&video_id=8uzNMMxuXOw&feature=vm The rules for 2 and 5 are both aimed at younger audiences. When you start to use an algorithm for division, then you can access this rule and make sense of it. I want all young kids to learn that you can spot this, then it doesn't seem like some great revelation later on when they are doing prime factorizations, because then, there's a bunch of rules to take on-board. Better to do it a little bit at a time. I hope that helps.

[@firlim]

Thank you Mrs @LadyDMcollector for your quick answer, I am GRE candidate brushing up on my math skills, so I need to understand more the rules of divisibility for 11, 13 and up if there is, thanks a lot !

[@LetsDoMath]

For 11, you can add, then subtract single digits in a number, and if the result is zero, or a multiple of 11, then 11 is a factor. Example: 10395 Break it into alternating positive, negative digits, left to right, then do the math: +1-0+3-9+5 = 0. Yes, 11 is a factor. 10395/11=945 The thing is, with divisibility rules for larger numbers, the rules get cumbersome and are more awkward than just pulling out your calc and trying it. I find them kind of brain-cluttering, the more convoluted they are. I don't generally give them brain-space. If I have to, I will refer to a note on this, but I retain the ones I am likely to use (2,3,5,7) For the GRE exam, are you not allowed a calculator? In the test prep for this, are you seeing questions where you are thrown a large number and required to state whether it is divisible by a particular prime, without a calculator or any working out paper? Do you know how to do short division? That will save you a ton of time on a question like this!

[@firlim]

We have an on screen calculator and a scratch paper but we are advised to not use them and to do more mental maths because of the limited time for each question. I am at my first prep days and I'm not sure whether or not we'll have those type of question during the test but I am encountering three digits prime factorization questions in my prep book, so I am looking for shortcuts that can help me save time

[@LetsDoMath]

3 digit prime factorization should be ok. Use whichever method you find easiest to extract primes. For myself, if I spot the value in my tables knowledge, I have an 'in', so I'll do a factor tree. If not, it's repeated short division. I ALWAYS go for the obvious small prime divisors first, and I use them till they are exhausted. Why divide by 13 if you don't have to? Check out the multiples of 13: 26 (div by 2), 39 (div by 3) 52 (div by 2), 65 (5), 78 (2), 91 is the first one you actually have to divide by 13. My advice on prime factorization is to have a crack at some for maybe half an hour, settle on your method and apply it rigorously. And do like I do...ALWAYS use those smallest primes first. I don't advise you to learn divisibility rules for 13, 17 or 19, as I expect you will chop down your number with smaller primes and then when you can't go any further, instead of doing a mathematical dance of convolution (and possibly mistake-making), when you get numbers that don't fit, you USE that on-screen calc and quickly try - is it divisible by 13? 17, 19, 23, 29? Seriously... don't get clutterbrain trying to cram this stuff. Use your noggin and time wisely and go for the fastest approach. Best, Ginny

[@acy1335]

Thank you so much for this I didn't knew how to do the reminder thing.

[@LetsDoMath]

For an easy look at how to think your way to a remainder, take a look in my Division playlist, at the vid called Short Division with a Remainder. I'm teaching this to a grade 3 class next week! Two of them told me they won't be able to do division (I think they've heard about LONG division), but I think they will kill it with short division. I just hope their parents don't tell them it's 'wrong' because they may never have seen it.

[@acy1335]

@@LetsDoMath Oh my god I have done division all along to find the prime factors now I can find them in matter of seconds I have mastered it thank you. May God bless you

[@LetsDoMath]

​@@acy1335 Ooooh! I LOVE this comment. How come nobody has shown you this yet? Wait... Are you saying you've been using LONG division to do this? If so... eeek! I'm surprised you're still upright! So... yeah, you can use SHORT DIVISION! You can see why it's my preferred way to divide! After doing this vid, I made a couple of others on Finding All the Factors of a Number. In those I just went at it more naturally - the moment you hit a value whose multiples you know, you can switch to the tree method then you can nail those primes in a few seconds! That's the benefit of having a bunch of math tools in your 'toolkit', so you can pull the right one just as you need it. There's always more than one way to solve a problem. If you've only been shown a single way, I feel bad for you, it's not meant to be that way. Well, not in MY opinion anyway. 😉🤗🤩💕

[@oo-zv6yd]

Thank you very much! This will help me in my activities.

[@LetsDoMath]

You are welcome!

[@meenavadrevu8415]

Thank you it helped me a lot

[@LetsDoMath]

That's great! Thanks for letting me know. :o)

[@sumanabhi9022]

thanku ma'am easy trik ke Liye thanku thanku thanku maam

[@LetsDoMath]

Great, Suman! I am so happy you got it!

[@tdbgaming5643]

Thanks for making it easy for me

[@salmabibi-dl9ym]

Very well defined

[@arberielajqi2046]

This was awesome. Thanks for sharing

[@LetsDoMath]

My pleasure. Happy to help. 😃🤗😎💕

[@arnold80s94]

Wow this is good. Thank you

[@someshpatil5243]

Very good explanation in very short method

[@shourya9680]

It's very easy trick thanku so much for your help☺☺

[@LetsDoMath]

My pleasure! Glad to help 🤗😃😎💕

[@shourya9680]

@@LetsDoMath 😃😃

[@sahilsharma2506]

Thanks a lot

[@LetsDoMath]

You're very welcome. :o)

[@matthewliu5161]

Hello! Excellent Tutorial, but for numbers like 36661, the smallest factor is 61, and we are left with 601, which happens to be a prime, but using your rules would not be effective. Is there any way to look for these numbers?

[@LetsDoMath]

Hi there, thanks for your note. This is the best method I know for pulling all the primes. I feel that for student use in school it is just what’s needed to work with larger numbers, however it does have limitations as you’ve discovered. This is where the art of the teacher comes in. In my view, teachers should come up with numbers that LOOK demanding, but are actually created through combining smaller primes, and only one prime above 17 and up to 97. The solution should be achievable, using this process. If a teacher is doling out numbers like you had that uses 61 and then leaves you with 601 at the end, the students will experience panic, math-sweats and a feeling of impossibility, followed by failure. What benefit does that have? I make numbers to break apart, by starting with smaller prime combinations, whose rules of divisibility kids can spot, then I tack on a x19 or x41 or something at the end. The point of that last... do they also spot it as prime? I am a very reasonable person. I don’t ask kids to do anything I’m not willing to do too. The number you had at the start... as soon as I hit a block where I couldn’t go any further, I’m not going to swear and struggle through it, I will use a computer and discover a nasty number was given in the first place. I think our job as teachers is to encourage and empower kids through learning, not demonstrate what they can’t do. I hope that helps you see my position on this. In formal exams I believe the values created for larger prime factorization are generated as I have described too. 😃😎😉💕

[@matthewliu5161]

@@LetsDoMath Thanks! I will be going to 7th grade next year, and I was just curious on what would happen in that case, but you are totally right. Personally, if I was a teacher, then yes, something like 36661 (which a University Math Professor came in and asked us just for fun, that was not the main topic though) would be unreasonable. Thanks for your note BTW!

[@kriptik_kid]

Thx so much for makin this topic clear for me . Now I understand . Th. Fam ..♥️🙌

[@LetsDoMath]

Happy to help, glad you get it now. You can combine this with the factor tree approach if you like, once you get down to a number whose factors you know. That will finish off the prime factorisation in a few seconds.

[@vaiga.s745]

thank u so much mam it was very helpful ,... u got a new subscriber

[@LetsDoMath]

Sweet! Glad I could help. Have you been on my website, letsdomath.ca that will help you find what you need quickly. 😃😉😎

[@anjanav5636]

I study this prime factors in your chennal😁😊😊your so good at math

[@LetsDoMath]

I’m glad if I helped you, way to go! 😃🤗🥰

[@anjanav5636]

😊😊

[@mehreenasif1674]

Thank you soo much mam i really enjoy your videos...🤗

[@purnimak9405]

Thanks to telling easy way

[@LetsDoMath]

It's my pleasure to help, Purnima. Thanks so much for your note.

[@pianomatt715]

Thank you! Always struggle with getting this process under 60 seconds for the GRE. Need some work on my end.

[@LetsDoMath]

Short division will get you there as I doubt they will give you really big numbers. But for speed, get it to where you recognize a value in your tables knowledge then switch to factor tree because it is quicker. Less marks on the page and more fluidity of the thinking.

[@skydragon3857]

cool, thanks Ma'am

[@LetsDoMath]

You're welcome, Sky Dragon. Are you blazing fast with this stuff now?

[@ItashaDutt]

LadyDMcollector yes ma'am

[@zeze3949]

😍 thanks

[@LetsDoMath]

😃🤗👍😉😎

[@shrisunilpawar]

Thank for helping me☺

[@LetsDoMath]

Thanks for your note, Sunil. My pleasure to help. :o)

[@riruru1722]

what abot 126053 you would thinks its prime but its factors are 233 and 541 . this is a problem i've face in my exams

[@katharinedimoski3069]

Thankyou this helped me heaps!! Could you do a video on the square root of big numbers too that would help heaps!!☘ Or if you could explain it to me that would be great thanks so much for this video i love it

[@LetsDoMath]

Hi Katherine. I have a couple of videos that may help: Square Numbers for Beginners, and Introducing Square Root. I haven’t done a vid on square root of big numbers because the most important understanding happens with smaller values - those in our tables knowledge. I feel that once you’ve got that understanding, when faced with bigger numbers, you’re either going to estimate the square root (I have a vid on that), or you’re going to use your calculator to find the root. I hope that makes sense and you can follow my thinking. It isn’t in my plan to make a vid on square roots of bigger numbers at this point, I’m afraid.

[@dakshayanimasilamani977]

Can u say me other examples and divisiblity mam excellent mam🙂🙂🙂😎

[@LetsDoMath]

There is another film too with a different example in the playlist Factors, Prime Factors

[@PankajKumarindia]

fast fast fast,, thanks.

[@LetsDoMath]

My pleasure, Pankaj! Thanks for your note.

[@suryar6979]

U made this one Very easy. Thank you so much.

[@LetsDoMath]

Nice! Thanks very much. And actually you can go even faster! The moment you get an answer which you recognise from your tables knowledge, you can flick into factor tree mode and finish it in seconds!

[@yug5489]

TOOOO HeLpFuLLL

[@LetsDoMath]

Thanks for this! 😉😃🤗

[@almeidacrushers243]

it's very helpful for me now

[@sahilsharma2506]

I love the way to make the concept understand to students

[@LetsDoMath]

My pleasure to help. Thanks for your note. :o)

[@JMartinez69261]

For basic learners I'd prefer to do them in order: 2,3,5,7,11,13..97. (She does 5 before 3.)

[@JMartinez69261]

And for four digits you need to go to 97. For five digits you need to go beyond what I have memorized. (A little Google play - you need to go to 313 for five digits.)

[@LetsDoMath]

I don't feel it necessary to go in order. I feel students should go where their brains show them the intuitive path. If I have a value ending in 5 I'm totally going for 5, and not scratching around to see if 3 is a factor. Intuitive flair from knowing divisibility rules and 5 is faster to spot than 3.

[@sketchyff6604]

You are too good

[@LetsDoMath]

Thanks very much, I’m happy to help. 🤗

[@akshaydeogaonkar7120]

You said we have to know divisibility rule of smaller primes... I ask you, for how many prime numbers exactly up-to we have to know the rule?

[@LetsDoMath]

Good question. You need to be able to see that a number is divisible by 2, by 3, and by 5. 7 will become obvious as you get the number down in size (you'll see a number in the 7x table). You also need to know your 11x table for the same reason. It's useful to know that 13x13=169. And that should be good for school use. 😃😎😊🤩

[@akshaydeogaonkar7120]

@@LetsDoMath Maybe you didn't understand my question... I expected the answers, up to 29... up to 31, up to 37 or up to primes less than 50...

[@LetsDoMath]

@@akshaydeogaonkar7120 This channel really deals in stuff up to the GCSE exam. The primes you mention, 29, 31, 41... those would all be left at the end of a prime factorization. You wouldn't learn multiples of 41... 2x41 is 82, divisible by 2. 2x31=62, 2x29=58. I expect people to take the easiest route to prime factorization, and that means using 2 as far as you can (for even numbers), and 5 if a number ends in a 0. Once a number has been knocked down in size, it becomes easier for students to spot a value from their 3x, 7x or 11x table knowledge. That's how I expect students at this stage to approach a prime factorization problem, using the least amount of memorization possible. I hope that answers your question.

[@akshaydeogaonkar7120]

@@LetsDoMath Thank you for your prompt replies... However, let me elaborate to you what my concern is actually... Consider the number 2209... Now, it's not a prime number as being square of 47... So, it has only three divisors i.e. 1, the number itself(2209) and 47... Hence, prime factorisation of 2209 can be expressed as... 2209 = 47 x 47 There is no number less than 47 is a divisor of 2209... In this case, we had to test divisibility for all numbers from 2 to 47 until we got divisor... However, it is too much time-consuming... So, I would love to know if there are any shortcut and optimum methods to factorise numbers like this?

[@LetsDoMath]

@@akshaydeogaonkar7120 I don't know of a shortcut and guess and check is so time-consuming as you said. So... my honest answer? This question has no place in high school, or on a test of whether people can do a factorization or not. The second part to that is if we really DID have to solve this one, I'd do what any regular person would do, and that is to google 'find the prime factorization', enter my number and discover it that way. That's when you find out the teacher is pulling a superiority stunt. I don't think high school math should be a way for a teacher to prove how much smarter they are than a student. I think questions should provide reasonable opportunity to show whether someone can handle a method and get to a solution. If there is nothing you can spot as a divisor for a number to start a prime factorization then I absolutely think it's a reasonable response to google it. But any number I'd give for a prime factorization question would feature 2,3,5, 7, 11 and maybe ONE other higher prime (anything in the range under 100) to finish off. Given that a question is created with a mix of these primes, there's no reason to resort to Google, because there is always a way in that you can spot, IF you know your rules of division. ;o)

[@CubeAK47]

Very helpful

[@roctionastre4015]

Thank you sooooo much ma'am this is going to help me sooo much!!!!!

[@LetsDoMath]

That's GREAT! It may well be that you never get a big number in an exam, but if you do, you're not going to sweat, because you have a strategy! You know multiple ways to do a prime factorization and that is ALWAYS stronger than just 1. Good for you!!

[@mridulaghosh5774]

Thank you very much.

[@LetsDoMath]

My pleasure! Glad to help 🤗😃😎🤩

[@toptips2484]

Thanks a lot ma'am...it was sooo.... helpful

[@LetsDoMath]

You're most welcome 😊

[@89_kosikisingh8]

You made it very easy

[@LetsDoMath]

Glad to help 😃

[@aishwarya0201]

Very nicely explained, Thank You Very Much🙏

[@LetsDoMath]

You're most welcome

[@Niyacrochets]

thank u

[@gaslitgirlboss]

You're a wonderful teacher! This video has helped me with what I couldn't learn over the course of 3 days, I'm subscribing to your channel and look forward to more of your videos ! Thank you..

[@LetsDoMath]

Thank you very much! I’m so happy you get this now. If you want to really get impressive with your prime factorization, you can combine the division method here... with the factor tree. As soon as you hit a number whose factors you know... let’s say you get 81 as the answer when you are dividing, well then you put a tree starter and say that’s from 9x9 and 9is from 3x3 and suddenly you finish it in a few seconds instead of doggedly going all the way to the end with division, like I did here. I think perhaps we might need to get used to that before gaining the confidence to switch partway through the prime factorization, but it’s an option, whenever you’re ready. 🤗💕😃🤩😎

[@ParallelMinute]

Then how about the divisibility rules for the other primes?

[@LetsDoMath]

For the level I’m thinking of (GCSE and below), knowing the rules for 2,3 and 5 are enough. Students are expected to know their tables solidly so that an element from 7s or 11s is easy enough to spot. I would only expect a single bigger prime to occur, and that will be left at the end. I would not expect to see 17 and 23 occurring in the same prime factorization.

[@Introvert4life_]

THANK YOU

[@lopamudrasahoo5057]

Great job...I'm very thankful to you

[@LetsDoMath]

My pleasure! Glad to help. 😃🤩🤗

[@rsxfazle]

@Let's Do Math Can you make a video for Prime Factorization for 6 digits?

[@LetsDoMath]

Nah, I’ve covered this enough. You can extrapolate from here. 😉

[@JEE_lakshya]

Thank you so much

[@LetsDoMath]

It's a pleasure to help 😃

[@vedanshgamer2.061]

If a no. Is not dided by numbers upto 20 so how we learn next tables suppose slove 23805

[@LetsDoMath]

First you divide by 5, because it ends in 5 so 5 is a factor. Whittle it down to size, bit by bit using whatever prime factor is the next obvious divisor.

[@nasimahmed8197]

Please give me the solution of 24965

[@LetsDoMath]

Hi Nasim. Who gave you that one? It was incredibly mean! Obviously you start with 5. That gets you to 4993. A quick check reveals it is not divisible by 3. I kind of cheated there. I didn't go and check 7 because I had a hunch. I used an online calculator and 4993 is a prime number! Seriously, people giving out prime factorization problems should be getting kids to a success point, not a block point like this. You are not helping kids. Feel free to have a prime up to 100, but beyond that IMO is a bit stinky. All you're doing is encouraging them to go straight to an online calculator. Please think about your problems before assigning them.

[@Motivationlife5491]

Your method is awesome

[@LetsDoMath]

Glad you like it. This method sticks to itself the whole way through. In the vid on finding all the factors of a number using prime factorization, I get a bit more relaxed with it. The moment I get to a number that’s in our tables knowledge, I flick to factor tree mode instead and finish it in a couple of seconds. But you should do whatever feels comfortable to you, and as long as it works, and you and your teacher can understand it, it’s all good. 🤗😎🤩😉

[@debateclub6]

Please answer me. How will I factorize 2666 into prime factors ?

[@LetsDoMath]

Sorry for late reply... This is a stinker. Not an example I would expect a teacher to give. First you divide by 2 and get 1333. You're stuck. So here's what I did: I searched up 'prime factor finder', picked a site and plugged it in. 2x31x43. Who the heck creates THAT number for a student? What's the lesson? The teacher knows more, or the teacher's a total meany-pants who wants the students to feel stuck and not able? My take on this: 2666 is not a number you should give to students in school, unless you want them hitting up the web for an answer. Problems are supposed to offer enough challenge to make you think, not be unmanageable, like this.

[@nickgill6639]

Can you also explain prime factorisation for more prime numbers

[@LetsDoMath]

Hi there. I feel like I have given enough examples in factor tree, by division, and one hybrid of those two strategies in my vids on finding all the factors of a number by prime factorisation. Now I want you to apply that learning and go after it for yourself. 😉🤗😘

[@himanshisharma8354]

Is this method only for 5 digit numbers ?

[@LetsDoMath]

No. You can use it to find prime factors of various length numbers. My example is 5-digit because I felt that was great enough to prove it works for most applications people may have, particularly in their exam preparation phase. I want people to be completely confident they have the tools they need to ace their exam.

[@maltiyadav5033]

Thank you mam you explain best

[@varunkumar-oe4ng]

thank you so so much

[@LetsDoMath]

My pleasure 🤩😃😎

[@vinodhkumar7205]

Tks mam

[@LetsDoMath]

You're welcome. It's a pleasure to help. :o)

[@kykyyvyv]

Is this only on 5-digit numbers?

[@LetsDoMath]

Not at all. It’s just a demo to show that any number your teacher gives you in school should be manageable. Of course, they probably won’t give you a number this big, and it shouldn’t feature 2 hard to work primes like 41 and 43. One is ok, because you will be left with that at the end, and have to realise it IS a prime to finish the problem.

[@swapnachowschundru5856]

If divisors are 2×3×3×3×5 means the expansion is 2×3cube×5 I am I write or wrong...

[@LetsDoMath]

Correct!