Divisibility Rules

[@johnwalker9817]

Michael: "It's so important to unify, but today we're going to divide." *Starts multiple civil wars.*

[@thenixaless7493]

Yeet

[@vividandlucid]

Hey Vsauce, Michael here. As we all know, slave trade is unhumanitarian and unethical, and we should band together to abolish it. *Or should we?*

[@hueban1643]

fun fact: division in Swedish is called "bråk" which also means brawl or fight

[@PuckishAngeI]

Hey Vsauce, Michael here. You probably think that Iraqi government is stable and legitimate, well think again, there are multiple claims and today we are going to ignite them and see how many new countries will pop up on the map.

[@TheEricwn]

You mean divisible civil wars

[@user-uq4gr5nl5o]

This turned into a math channel so progressively that I didn't even notice.

[@danielmcdaniel1250]

JJJ he’s literally numberphile rn

[@cheesycheese60]

It was supposed to be a channel with fun links in the description

[@Ptaku93]

@@cheesycheese60 maybe 5 years ago

[@cheesycheese60]

@@Ptaku93 u know time goes fast

[@alevanderBatman]

@@Ptaku93 Well... no. The name literally means "Do Online Now Guys".

[@alexgabel4379]

Schools: *close* Michael: ...or do they???

[@Kitsudote]

*Vsauce music starts playing*

[@Cowonahill_]

Sh1pp0K1tsune It started playing before I even read your comment. X)

[@TuhinBagh]

DING!!!!!!!!!

[@dewifrancis1299]

My literal exams: Cancelled Michael: Or are they?

[@dewifrancis1299]

@@TuhinBagh dong

[@yigitaganoglu188]

Michael: Is 80 divisible by 4? Me: I don't know. Let me ask my French friends...

[@gonderage]

hon hon, it is la weed nombre.

Michel just missed a great opportunity to speak about ... you know, the big white Elephant in the room... THAT.

[@user-xw4mu6nz4t]

How to get your maths answer: 1. Ask any asian friend (preferably Chinese or Indian) 2. If that doesn't work ask your teacher... 3. You're in a test? Try and remember this video you watched 9 months ago 4. Wait... nvm I can just Google it...

[@ashleybyrd2015]

@@user-xw4mu6nz4t and if that doesn't work be inspired by the meet the engineer SFM and solve it with a gun, and if that don't work try more gun.

[@gwenrees7594]

Quatre-vingt ;)

[@joshfromjuniorstudios]

The hero we need right now, but not the one we deserve...

[@Equa11ysurl]

Junior Studios Nobody truly deserves Michael..

[@sean..L]

why is it in past-tense?

[@gumunduringigumundsson9344]

Mister past tense there is probably feeling lonely. Be kind.

[@ChristakyMe]

deserve*

[@アヤミ]

Guðmundur Ingi Guðmundsson ok boomer

[@movedlonely_space_egg1169]

"divisibility rules" glad to see micheal sticking up for the underrated mathematical operation

[@turtles10]

lonely_ space_ egg I’m more of a fan of roots

[@deaddead698]

Tristen Roddenberry idk man it’s all about quadratics imo

[@ihateroads7926]

Pepper Mint Nah logarithms are where it’s at

[@JonnesTT]

Excuuuse you princess. Division is probably the most rad basic mathematical operation

[@JonnesTT]

@uwau cube root of 24 the 2.88th Reich :D

[@elixir4419]

11:46 “179200 I just made this one up” people he can create numbers he’s more powerful than we thought

[@Bballenjoyer]

Wat

[@LeafShade]

@@Bballenjoyer Until he made it, 179200 did not exist.

[@joshuaslattery2416]

@@LeafShade tbh i never thought about 179,200 before this video so id believe it.

[@mathscienceonlineacademy4512]

Exactly

[@pikchassis]

The other number was a decoy!

[@RaynbowIsMe]

BRO when I was in elementary school we did all of these except we got told “there’s no rule for divisible by 7” they LIED!!

[@davidcole2913]

No, it’s just that no one had come up with one back then. And honestly, the trick that Michael shows in this video isn’t a quick rule at all. Very time consuming. At that point it is faster to just divide the number by 7.

[@thepriestunknown3999]

15:38 here we are

[@nitaibaishya6374]

We were told that it was too critical for us so they excepted...

[@jeffw1267]

@@davidcole2913 I have a book from 1960 that shows a divisibility by 7 rule, though it's sort of complex. You have to match up six digits in the number to the series 132 645, working from the rightmost digit first. If your number is larger than six digits you start the 132 645 series again. Each digit in the series is multiplied by the corresponding number in the answer. For 362,880, working from the right, you'd get (1x0) + (3x8) + (2x8) + (6x2) + (4x6) + (5x3) = 91. Then you divide THAT by 7 and get a zero remainder. I think it's easier to just divide the number by 7 straight through, especially if you are doing the problem mentally.

[@indigofenrir7236]

@@jeffw1267 @jeffw1267 Double the last digit and subtract it from the remaining digits. Ex. 434 => 43 - 2(4) = 35, which is 7x5, so 434 is divisible by 7. Using Michael's method, 1/10(abc - c) - 2c 0.1abc - 0.1c - 2c 0.1abc - 2.1c 10(0.1abc - 2.1c) = abc - 21c 21c is just 7(3c), so it checks out.

[@gabry_infernape]

Schools: *close* Michael: Fine, I’ll do it myself

[@xkilla911]

this is a lesson on "discrete math" from college by the way.

[@monkie2464]

Fine, I'll do it BETTER myself*

[@hellomine2849]

ngl I learned new interesting stuff and I'm in high school

[@-ahvilable-6654]

He will not divide us

[@Т1000-м1и]

990 likes

[@atomicbomber2000]

There's a trick for 7 that's even easier: Separate the ones digit from the rest, double the ones digit, then subtract the 2 numbers. Here are some examples 903 separates into 90 and 3, double 3 to get 6, 90 - 6 = 84 which is divisible by 7. (903 = 7 x 129) 3171 separates into 317 and 1, double 1 to get 2, 317 - 2 = 315, which splits into 31 and 5, double 5 for 10, 31-10=21 which is divisible by 7. (3171 = 7 x 453) Note: If this process gives you 0, the original number is also divisible by 7

[@MrGamingANDfootball]

This is the one I know

[@ireallydontknow3299]

Oohhh, this is interesting. I suppose this is because adding -2 is the same as adding 5 modulo 7. As far as 7 is concerned, this is essentially the same as adding 5 times the last digit. Brilliant!

[@angelmendez-rivera351]

eventhorizon51 The reasoning is very similar. I am going to use three digits for the sake of simplicity for this proof, but it trivially generalizes to any number of digits larger than 2 via induction. Any 3-digit number is given by x = 100d(2) + 10d(1) + d(0), where d(i) is between 0 and 9 inclusive, except for d(2) excluding 0. The proposed method is 10d(2) + d(1) - 2d(0), but it works because 10d(2) + d(1) = (100d(2) + 10d(1))/10 = (100d(2) + 10d(1) + d(0) - d(0))/10 = (x - d(0))/10, and (x - d(0))/10 - 2d(0) = x/10 - 2.1d(0) = (x - 21d(0))/10, and 21 is divisible by 7.

[@randomnpc445]

This is also a much more useful shortcut if for some reason you don't have a calculator on hand. The one shown in the video is cool and all, but it's not very user friendly for larger numbers, not to mention having a bit of a complex process to it. This is a lot simpler and easier to follow.

[@ireallydontknow3299]

@@Aw3som3-117 I suppose only having to multiply by two will generate easier computations, so it might be slightly easier and faster than Michael's method.

[@knicklicht7945]

Michael looks like he already has been in quarantine for 5 months

[@squibble311]

he never met other humans, he was always in quarantine

[@OceanRedux]

BRUH LOL

[@observingatoms]

He was in prison

[@Retard634]

@@observingatoms based

[@Gluis-g6w]

actualy 12 years

[@Eduardo_G]

Michael is starting to look like Charles Darwin with that beard

[@thatladoverthere7075]

Charles Manson*

[@jellyman0127]

Well, he is the next step in evolution for humankind.

[@thedoctor855]

Michael is Charles Darwin reincarnate

[@VoiceDisasterNz]

Or Friedrich Engels

[@truediamant777]

Yes he is almost ready for the prophecy

[@TheSektorz]

Michael looks like he's been isolated since way before this epidemic

[@Megalomaniakaal]

So do I tho. Oh wait. But I have been isolated for far longer. Never mind...

[@vanzwho854]

He has prepared for the random chimp event well. This man will leads us to victory against the chimps

[@apersonontheinternet7607]

Mind Field S1 E1.

[@buttercopter9369]

*pandemic

[@macbeth8393]

That would explain the 25 minute video on divisiblity rules... this man is clearly going insane

[@prenomnom5304]

It took a pandemic to see him around again on this channel. Nostalgia for isolation Michael???

[@grampton]

Blue Shirt Wow bruh it didn't appear on my sub feed

[@thealphas1]

Damn we should have these pandemics more often

[@spaghetti7929]

it’s not nostalgia it’s trauma

[@sy7028789]

Not related message from a random Hongkonger for anyone watching: Remember the Virus is creating in China, it is all okay to call it China Virus. Never trust WHO cuz it is controlled by CCP.

[@ChrisTian-mf8wu]

Thank you for explaining not only "how" more importantly "why".

[@xystem4701]

I love how earnest Michael is. Keep making the world a better place

[@kfdhbdj9224]

What is earnest?

[@drdoof2940]

@@kfdhbdj9224 ear·nest1 /ˈərnəst/ adjective resulting from or showing sincere and intense conviction. "an earnest student"

[@LSK2K]

@@drdoof2940 you use reddit by any chance?

[@KariMusic0116]

Michael: Lets pick a random number also Michael: **picks a number divisible by all numbers 1 through 9**

[@kickowegranie3200]

he could have gone with smaller one, 7! (5040), it's also divisible into all the numbers 1-9 but it's much much smaller

[@dzarko55]

@@kickowegranie3200 Or an even smaller number, 7!/2.

[@schrodinger6991]

I think Micheal found the number himself and did not Google it. This is why he picked it I think.

[@deidara_8598]

@@kickowegranie3200 That is true, because 8 and 9 are not primes, and can thus be written has factors of the previous numbers, thus 7! is divisible by those as well.

[@onemadscientist7305]

@@dzarko55 which is the smallest (2520).

[@waiitwhaat]

Amateurs- "Number" Heroes- "Numerical" Legends- "Number in base 10" Michael- "Spelling of the number" (2:28)

[@tap20]

Spelling of the number in base (20/5) +(2*3)

[@SLAMgamer11]

Mathematicians - n, such that it is a member of a set R

[@dhruvamehrotra1975]

Well, technically they are digits.

[@jackholmes7003]

@@tap20 Base 12?

[@luiginotcool]

@@jackholmes7003 check again, it equals 10

[@AA-100]

Divisibility by each number: 2: Number is even i.e. last digit is 2,4,6,8,0 3: Sum of digits is a multiple of 3 4: Last 2 digits divisible by 4 5: Last digit is a 5 or a 0 6: Number is even and Sum of digits is a multiple of 3 7: Take 5× last digit and add to remaining digits OR take 2× last digit and subtract from remaining digits. Final total divisible by 7 8: Last 3 digits are divisible by 8 9: Sum of digits is a multiple of 9 10: Last digit is a 0 11: Alternate between Adding/Subtracting digits from left to right starting with Subtracting. Final value is 0 or divisible by 11 12: Last 2 digits divisible by 4 AND Sum of digits is a multiple of 3

[@It-b-Blair]

😮🤯

[@zafnas5222]

@natant927 It's because 6 has a factor of 2 ie. 6 = 2 * 3. This means that if a number is divisible by 6 then it must be even so it doesn't make sense to repeat the divisibility by 2 rule

[@That_Funny_Guy69420]

The divisibility rule for 7 only works till the 14 multiple.

[@WakenerOne]

Michael: "In times like these, _we need to be _*_unified."_* Okay, how many people immediately said, _"Or _*_do_*_ we?"_

[@OceanRedux]

guilty as charged

[@WildStar2002]

@@OceanRedux me too!

[@antonioocchipinti801]

Ok I'm kinda embarassed to ask this but... so I'm pretty good at english becouse I'm learning it since I was 6 but I still don't understand what "Or do I" meme means

[@WildStar2002]

@@antonioocchipinti801 No need to be embarrassed about that! It's something Michael say A LOT in his videos. That's all! 😃 Watch a few more from VSauce and you'll see what we're talking about!

[@onedarthyear726]

antonio occhipinti the ‘or do i?’ meme uses sarcasm. Sarcasm is a type of humour that becomes funny by doing something unexpected. Like saying (insert random dictator here) did nothing wrong. The joke teller doesn’t think that that person did nothing wrong, but its so unexpected and rude that it becomes funny.

[@leg1t343]

He's acting like he didn't leave us hanging for 7 months

[@ckv954]

- Leg1t Lmao

[@peppermintmiso4341]

He did have the holes one on Vsauce

[@chugggs3516]

Oh god I've just realized as well

[@AldraineGarcia]

It has been four years

[@bertiljohansson5665]

Just gonna leave this here: 10:18

[@nickb8507]

Bertil Johansson has oooh ooooooh 😫

[@LeonStevenWilliam]

20:23

[@santicruz4012]

Thank you

[@zmirburger]

thank you this has changed my life

[@caritahearts2405]

Vsauce out of context 4 babeyyy

[@breadleymcthicc5444]

Vsauce is that one mad scientist that makes everything fun, but at the same time everyone suspects him of being on crack.

[@noctusion2392]

Same for Micheal Reeves tbh

[@ActionJackson669]

Maybe to people who have never seen a real crackhead before 😅💯

[@w花b]

@@noctusion2392 nah it doesn't feels the same he's crazy in his own way

[@Fascist_Femboy]

wait he isn't on crack?

[@hoseamathews5791]

​@@Fascist_Femboyor is he

[@noahwilliams8996]

Other youtubers: "Corona virus!" Clearly superior vsauce: "divisibility tricks"

[@mrghostlyr1162]

Yup, let's study to keep graduation possible (ahem homeschool) - internet available - free will available - no teacher peeking for rule breaking - school rules : no rules, games

[@CraigC55]

If people ate right they wouldn't have to worry about any virus.

[@mrghostlyr1162]

@@CraigC55 Well, then people must feed animals the right way, make special meal schedules, and redo the FRIKKING BIOLOGI, viruses are here because they are predictors too, imagine life 200 000 years ago but in the kingdom of bacteria, viruses, cells, whatever nothing has changed

[@CraigC55]

@@mrghostlyr1162 Viruses thrive off of bad cells. If you have been eating dirty for years, you will be a breeding ground for illness. If you remove the bad cells, virus has nowhere to live. Minimal place to live at best.

[@noahwilliams8996]

@@CraigC55 That's not how it works. At least not with corona virus. Corona virus will infect your cells regardless of whether they're "clean" or not.

[@basantachaulagain6104]

"They allow us, in this lonely times, to make a bunch of new friends, math friends." --Michael, 2020

[@tracyh5751]

At first I thought he was talking about all of us watching this video together. More and more, I am convinced that Michael is talking about the math itself. The math is our new math friends.

[@DucNguyen-rk8zu]

Yes

[@Tsai_tama]

Plot reveal : Michael is doing maths to avoid being crazy in his asylum

[@cinnabonbon]

Eh eh eh, no spoilers!

[@TheBEST-eg4yd]

MATH*

[@OmarBKar-sw1ij]

@@TheBEST-eg4yd It's called maths you American heathen

[@ViratKohli-jj3wj]

@@TheBEST-eg4yd It is called maths

[@DanielDiaz-zz6ih]

It'S cAlLeD MaFs! Words are words are words. Tyre and aeroplane are weird, though.

[@vandithsreenivas5966]

Two types of people: Those who write '8' in a single stroke Those who draw two circles

[@adamqazsedc]

I draw 8 with a single stroke, obviously.

[@squibble311]

the 2 types are 1. those who write it in one stroke 2. michael david stevens

[@TechnicFyre]

It just comes out as nicer looking when you clearly make two circles. Unless they’re too far apart... or an accidental venn diagram...

[@coltz-pun7871]

What if I drew the two other halves of it

[@possiple2126]

I prefer to make a 3 and a backwards 3, please, I have standards

[@Carbon_Crow]

Relevant trivia: The number 2520 is the smallest number that's divisible by 1-10. Edit: It also has many other interesting properties such as being: - half of 7! (7 factorial) - a highly composite number (if you don't know what that is you may want to watch this video: kzbin.info/www/bejne/aHuwY6J_osdsh8k) - a colossally abundant number (I've tried to find and video or website that explains it in an understandable way but I can't find one) - a Harshad number (a number that is divisible by the sum of its digits. Ex. 24: 2+4=6, and 24 is divisible by 6) - the aliquot sum of 1080 (a rare relationship between two numbers where the sum of one of their factors is equal to the second number and the sum of the factors of the second number is equal to the first number. If I didn't explain it well I recommend watching until 1:30 of this video: kzbin.info/www/bejne/jaXFnHWibMinaqs)

[@shoaibakhtar4389]

Thanks for info friend

[@shoaibakhtar4389]

@@sy7028789 but i think this was a conspiracy theory 😅 isn't it bro?

[@horizonkage]

Math is broken. 2520 single digits should replace 1-10.

[@woutervanr]

I always approve of Numberphile videos. Especially after receiving my piece of pie yesterday :)

[@Carbon_Crow]

@Wouter vanR I prefer Tau over Pi but I kind of feel bad for Pi this year; nearly everyone forgot about Pi day because of the coronavirus Edit: grammar

[@qwertism]

I wish I could divide Michael so I could have a part of him

[@davidsphere43]

Who says you cant?

[@deathbyseatoast8854]

@@davidsphere43 mhm, yes fbi thats the man.

[@thewj1228]

Psycho

[@noahgreer1497]

Or would you? *que music*

[@strbourne]

I call dibs on the left foot

[@randomgblsfs2190]

When Michael said that the random number is not actually a random number, I felt betrayed.

[@Speed001]

No number is truly random.

[@hellomine2849]

​@@Speed001 vsauce theme starts playing

[@WWFYMN]

@@Speed001 Or is it?

[@theneoreformationist]

I could tell by looking at it LOL

[@ayaanshaheen6604]

@@theneoreformationist It is 9! or factorial

[@sohamdey5124]

In Divisibility with 7, I subtract 2 x (one's digit) instead of adding 5 x (one's digit). It is easy to calculate and works!

[@A114N8D]

Came here to say the same thing.

[@inderchopra430]

We can create multiple methods to solve the 7 one. Like multiplying unit digit by 1.5 and adding it to the rest should also work bcoz 1.5 - 0.1 is 1.4 But using whole numbers like 2 or 5 makes more sense I agree

[@dorijanlendvaj8356]

You can also, for example if the number is abcdefgh, look at h+3*g+2*f-e-3*d-2*c+b+3*a. Basically, going from the least significant to most significant digit you just repeat 1, 3, 2, -1, -3, -2. Much easier to do than the method shown in the video. As a bonus, all the other divisibility rules also preserve the remainder when divided by that number(for example, the sum of digits of 582 is 15 so it has a remainder of 6 when divided by 9). The rule for 7 shown in the video doesn't preserve the remainder, but this one does(but keep in mind that the remainder of -1 is 6, not 1).

[@billborrowed3939]

10:18 I mean, come on. He just wants us to make memes.

[@qdudehome9889]

8:26 At this point, I heard the music

[@Andrew90046zero]

me 2

[@scmtuk3662]

kzbin.info/www/bejne/in-VZpqeoMuah6M

[@Jireninyourrecommendations]

I don't know if 49 is divisible by 7. Let me check that 4 + 9(5) -> 4 + 45 =49 Guess I'll never know

[@june349]

Know your 7 times tables, just like you should know your 8 times tables

[@jamieg2427]

o o o o o o o o o o o o o o o o o o o o o_ o o o o o o o o o o o o o o o o o o o o o_ o o o o o o o Seven rows and seven columns. Count the o's and then you've got 'em.

[@Dziaji]

Just keep doing the operation like Michael said to. It can take a while. Don’t give up!

[@user-en7dx1qp3k]

Do it the other way: 4 - 2*9 = -14

[@gumunduringigumundsson9344]

@@user-en7dx1qp3k that makes no sense at all lol.. you trolled my cranium there hahaha gj.

[@honeybee9455]

Mike: chooses 362,880 at "random" Me who watches numberphile: I see what u did there.

[@shadrackbrentuo3665]

???

[@honeybee9455]

@@shadrackbrentuo3665 the number has 160 divisors, is the factoral of 9, is a tau number, is pseudo perfect, etc.

[@honeybee9455]

@@shadrackbrentuo3665 basically all digits 1-9 are factors of 362880

[@shadrackbrentuo3665]

@@honeybee9455 Ooh. Thanks!

[@honeybee9455]

@@shadrackbrentuo3665 np

[@vevorjepo]

"in times like these, we need to be unified, but today, were going to divide." *avengers music starts to play*

[@Robbnlinzi]

vevor jepo thanos wants to chat

[@CryoCrow]

Me: Why does this work?? Teacher: bEcAuSe iT DoEs!! Michael: Weeelll. . .

[@Rygir]

That's not a teacher, or at least a terrible one

[@hafda010]

Шнат’s шітһ тһе шеігd теасһег сарітаls ?

[@Real_Eggman]

@@hafda010 Why are you writing in russian letters?

[@3bhma197]

Michael: "let's choose a random number" Michael: *choses 9!*

[@softlysnowing3959]

i know right

[@caleblewis8169]

He did it on purpose he winked i think

[@softlysnowing3959]

@@caleblewis8169 Of course, It's not like I didn't know I knew something fishy was going on.

[@br6768]

He writes 8's the same way I do!.. I always though I was weird but now I feel cool 😬

[@brownah]

Dwade : also chooses 9

[@spencermovies]

Michael! I though of a way faster method to check divisibility by 7: 1. Take the leading two digits of the number. 2. Divide by 7 and find the remainder. 3. The remainder becomes the new leading term 4. Repeat until you recognize the number as divisible by 7 or not. E.g. 362,880: Not sure if divisible by 7 36->1 12,880: Not sure 12->5 5,880: Not sure 58->2 280: Pretty sure 28->0 0: Divisible by 7

[@HarryBallsOnYa345]

"Why Did They Change Math!? MATH IS MATH!" - Mr. Incredible.

[@CallMeCarlos1]

"I'm going to pick a random number"

[@rmay2215]

*it's casually divisible by all numbers from 1 to 10*

[@alexandreman8601]

@@rmay2215 it's casually 9!

[@UnsIiced]

@@alexandreman8601 It'S nOt NiNe ThOuGh

[@alexandreman8601]

@@UnsIiced it's 9 factorial

[@FedeRama]

"but what is random?" -Michael, 2014

[@drifted3566]

D!ng dong Who’s there? Vsauce Vsauce who? Vsauce, Michael here

[@br6768]

Wasnt this channel called dong?

[@claytonbyrd6134]

@@br6768 it was, but KZbin wasn't happy about it.

[@aryyancarman705]

@@br6768 what dong? It was never called dong, trust me..

[@frostonium]

@@aryyancarman705 it did kinda called dong something you can Do Online Now Guys Before it was reffering to uhhh the thing and its called ding now. I think anyways lol

[@0bread286]

frostonium He was joking. As though the channel once being called dong was something that couldn’t be talked about.

[@MehtehTrollfacer]

Bonus divisibility rule: To determine if something can be divided by 11, take off the last 2 digits and add them to the remaining number. Repeat until you have something that you know is divisible by 11. Ex: 35,365 353 + 65 = 418 4 + 18 = 22 = 2 × 11 Bigger ex: 6,954,035 69,540 + 35 = 69,575 695 + 75 = 770 7 + 70 = 77 = 7 × 11 Explanation: Number abc, last 2 digits are bc. abc = a × 100 + bc The operation does: (abc - bc + (100 × bc)) / 100 Essentially, you're adding 99 × bc to the number, since 99 × is always divisible by 11. However subtracting 1× and adding 100× does the same thing, so you can use that instead.

[@snowfloofcathug]

Mehteh Trollfacer Thank you! Was disappointed that he didn’t show any unknown trick

[@akshayreddy9892]

Simpler method: Add the 1st, 3rd, 5th ........ digits together and the 2nd, 4th, 6th digits together and subtract the two. If you get a multiple of 11 or 0, it is divisible by 11. Ex- 35,365 Sum of odd digits = 3 + 3 + 5 = 11 Sum of even digits = 5 + 6 = 11 Difference = 0 Therefore divisible by 11

[@sanyalox01]

I have a more interesting trick. Just substract the last digit from the rest of the number. If the result is divisible by 11, then so is the original number. Ex. 35365 3536-5=3531 353-1=352 35-2=33 3-3=0 0 is divisible by any number except itself, so it's obviously divisible by eleven, and so is 35365

[@MsMangoChan]

@@sanyalox01 this entire thread is golden, amazing

[@kegtuwa]

1:36 "First let's pick a number completely at random" Michael lied as naturally as he breathed

[@shivamchouhan5077]

Literally 9!

[@Leonardo-G]

Not exactly a divisibility rule, but: To check if a number is prime, you only have to check all primes up to its square root. For example: is 103 prime? It’s square root is between 10 and 11, so check 2, 3, 5, and 7. We know it’s odd and doesn’t end in 5 or 0, and that 1+0+3 =4. The only one left is 7, which we test with the trick in the video: 10 + 5(3) = 25, so 103 is not divisible by 7 and is therefore prime.

[@akkok5059]

why do we check with 2,3,5,7? Sorry I'm not really good lol

[@Waouben]

@@akkok5059 First why do we only check divisibility with prime numbers? Because non prime numbers can be written as the product of prime numbers. Why is that? Because if your number is divisible by a non prime number, you can divide the factor once more until only prime numbers remain. For example, let's take 20. 20=2×10. But 10 is non prime which means you can divide it. 10=2×5. In the end, 20=2×2×5. You only need to check prime numbers to know if your number is prime. The only prime numbers below 10 are 2, 3, 5 and 7.

[@Waouben]

@@akkok5059 Secondly, why only check up to the square root? If your number is divisible you can write it as n×N, with n

[@MrManiakKomputerowy]

@@akkok5059 Because the rest of numbers between 1 and 10 are product of primes. Take the number 103 and check divisibility by 2, then 3. Now we have 4, but if the number is divisible by 4 then it's also divisible by 2 and we checked that already. Next comes 5, then 6 but if the number is divisible by 6 then it's also divisible by 2 and 3 - we checked that already.

[@anzahanifathallah]

i learned a lot of these as a kid and one favorite pastime of mine is to mentally add the digits on license plate numbers to determine whether or not they're divisible by 9 (license plates in my country always have a 4 digit number in them)

[@하람배-q5k]

I got quite confused by the "4 number digit" thing for a bit so I just wanna let you know you switched those around

[@sharabhojha7895]

Wait, so only 9999 people live in your country? There has to be some other combination of letters added in as well, right?

[@edgarsxdwoo7417]

yee in Latvia we have 4 numbers and 2 letters

[@anzahanifathallah]

@@sharabhojha7895 yeah the format is [one or two letters]-[four numbers]-[two or three letters]

[@anzahanifathallah]

@@하람배-q5k right lol

[@fresh-avocado]

I've been using these divisibility rules my entire life in school and never knew how they worked. Who'd have thought that their functioning would be so easy to understand. Thanks Michael, very cool 👏👏

[@justcuzbrosky]

There is something really cool in the inconsistency of Michael's writing. Sometimes he writes multiplication as an x and sometimes and dot. very cool.

[@JanMilavec]

he probs also holds the world record for the most ways to write an 8

[@GeorgTheGr8]

I bet Micheal is powerful enough to know what happens when you divide by 0

[@the_man_of_sex1427]

Hi

[@dysondyson9524]

Le Rebel Flagship an error message

[@renerpho]

I've heard when you divide by 0, Chuck Norris appears and does a roundhouse kick.

[@Lumens1]

Le Rebel Flagship it is infinity. You’ll learn about it in calculus when you go over limits

[@oswurth8774]

The answer is probably hidden in his beard

[@omarziada5]

Michael: now let’s see if it’s divisible by four. My brain: oh yes, we can half it twice. Michael: take the first number in the two digit number and double then add it to the second digit. Me:...

[@KaitouKaiju]

If half the last two digits is even, then it's divisible by 4 Seems way more straightforward

[@dylankrejci9965]

@@KaitouKaiju that doesnt account for numbers like 16. 6/2=3 which isnt even. but as we know 16/2=8, and 8/2=4 so its even

[@GRBtutorials]

@@dylankrejci9965 It's the last two digits, not the last one. For 16, it'd be 16/2 = 8, which is even, so it's divisible by 4.

[@steffen5121]

Try dividing 426,421,295,739,292,069,436 twice in your head to check. I know it is divisible by four right away thanks to Michaels trick.

[@TheArchoNils]

@@steffen5121 You don't get it. You only half the last 2 numbers and check if it's even >___>

[@LunaIsOnYoutube]

Michael would do for the best teacher He can easily explain what he understands so easily and smoothly God bless Michael

[@nicksummers8320]

My favorite part of my Number Theory elective in college was proving the divisibility rules for 3 6 and 9. They seem so not math-y when you learn them as a kid, but the proof is very easy to understand

[@june349]

For those of you who forgot the rules as soon as you stopped watching: 2: If the number is even, it can be divided by 2 3:Take all the digits in a given number and sum them up. If the resulting number is divisible by 3, the original number is divisible by 3 4: If the last 2 digits of the number form a number that is divisible by 4, the whole number is. OR. Take the 10s digit and double it, and then add to that the ones digit. If that number is divisible by 4, the original number is as well. 5: If the number ends in 0 or 5, it's divisible by 5 6: If the number is divisible by 3 and is even, it is divisible by 6 7: Take the 1s digit, and multiply it by 5. Then, add to it the remaining numbers as if it were its own number (the whole thing, not each individual digit). If the resulting number is divisible by 7, the original number is as well. 8: Take the hundreds digit, and multiply it by 4. To that, add the tens digit times 2. To that, add the ones digit. If the resulting number is divisible by 8, the original number is divisible by 8. 9: If the sum of all of the digits in a number is divisible by 9, the original number is divisible by 9 REMEMBER: All of these processes can be done multiple times if you are unsure if the resulting number is divisible by the number (1, 2, 3... ,9)

[@Idisagreethisisnotanon]

Matthew Riachi thank you soooo much!!

[@xythrr]

You forgot 1 help

[@june349]

@@xythrr Every number is divisible by 1

[@softlysnowing3959]

@@june349 Not True; Every Integer is divisible by 1, not every number

[@june349]

@@softlysnowing3959 I never said evenly divisible. I just said divisible

[@thaaamer1]

number theory , god they were the best 2 courses i ever took in the uni.

[@Epinardscaramel]

“I am dying to hear about it, since I always thought number theory was the Queen of Mathematics -- the purest branch of mathematic -- the one branch of mathematics which has No applications!” -Douglas Hofstadter, Gödel, Escher, Bach

[@exzyyd392]

Oh yeah! Michael is back OH NO, MICHAEL HAS BEEN LOCKED INSIDE FOR AN INDETERMINATE AMOUNT OF TIME

[@bekeba]

Flashbacks

[@Kalay0Fox]

chew

[@groetjesuitdehel]

that intro was some whiplash. Really cool of him to be so early on the social distancing train though

[@Rhino123freak]

I remember studying all these rules for aptitude exams. Really cool to see *why* they work though. Thanks for sharing!

[@g-rexsaurus794]

aptitude exam? What's that?

[@GreenGoblinCoryintheHouse]

I was required to learn this once when I was like 8 or 9. I haven't used it since then.

[@Rhino123freak]

@@g-rexsaurus794 CAT, GMAT or SAT examination for instance.

[@m.gaiolas457]

19:22 "Oh! Look at this!" A new meme is born.

[@lubomirkubasdQw4w9WgXcQ]

Clever.

[@nursmalik6024]

I like how he went so crazy that he makes these reactions on calculations

[@HI3Enjoyer]

Looks like I only knew a fraction of this topic.

[@fawzanfawzi9993]

Good pun

[@chrisheli1]

I don't have much to add here

[@mlgepicbanana69]

This made me laugh on *multiple* levels

[@HI3Enjoyer]

@Jacob Vachon no matter how hard you try to stop us all, there will always be a remainder...

[@hastley64]

when he said "let's pick a completely random number" the number 69 was just written on his face

[@OwenMichtofen-rx5yz]

We missed you Michael.. even if we can’t show it meaningfully. Stay safe brother.

[@aspire4more]

Thank you for uploading to this channel again, Michael. I really appreciate the hard work, and enjoy the videos. Stay safe out there

[@HipsterShiningArmor]

I wish Michael had talked about divisibility tricks for 11 because that one is super cool

[@Halbairn]

_All aboard in Michael's online classes!_

[@amgil475]

D Sauce your name 😂😂😂😂

[@averagemilffan]

Kimi no na wa

[@doctor_owl]

As someone with dyscalculia, this is INCREDIBLY helpful. I wish Micheal had been my math teacher! I need to understand HOW math works, otherwise it's too abstract for me. When I was a kid we were expected to just memorize everything by rote with zero explanation, so even as an adult I still struggle with basic multiplication and division. Logic and algebra make more sense to me, so this video is a life saver!

[@Cazador1]

It's Michael, not Micheal

[@jamieg2427]

Math should _only_ be about understanding how things work. There should be hardly any memorization at all. It sounds like your difficulty with math had more to do with poor teaching methods.

[@nijamagi1031]

I feel like my foundation for maths were scrambled by just that. We were always taught to memorize recipes rather than understand how they actually work. I wish I hadn't been taught this way.

[@doctor_owl]

@@Cazador1 Whoops, thank you!

[@coolkusti]

What if I told you this video *severely* overcomplicates things? I suggest reading about the cyclic groups and modular arithmetic. Makes all these results much more basic and really easy to extend to other numbers.

[@cboneperlstone9661]

“4.9 looks a lot like 49, a number FAMOUSLY divisible by 7”. I guess yeah it’s famous. It’s the only number twice as divisible by 7 as any other number divisible by 7. I guess 49 IS famous in the circle of 7.

[@Brenden-H]

famous in the circle of 7? I think you mean.. in the SQUARE of 7. Ill show myself out...

[@slimeypiston574]

@@Brenden-H Ba dum tss!

[@the_phoe]

@@slimeypiston574 Well, the only number twice as divisible by seven as any other number divisible by seven before 2401 !!

[@vampire_catgirl]

I go back and watch this video over and over again simply because the explanations for how it all works is absolutely beautiful, and of course Michael talking about anything always makes it better too

[@melodygrace2582]

Fun one for 11: if the number is abcde, then the alternating sum a-b+c-d+e is divisibly by 11, then the original number is divisible by 11

[@thesuccessfulone]

That little smile he put on the sheet c: it had no idea he would discard it like a merciless god exhausting the use of his creation.

[@nickoates]

I never thought I'd heard Michael say "Dong" again...

[@RandomPlaysGames2763]

Unlike the time he said "Ussie"

[@dawinsor87]

Michael thank you for all of your Vsauce, Mindfield and Ding videos! The content is some of the most fascinating stuff I've watched on the whole internet. Your method of presentation and your subtle humor makes for a really enjoyable experience.

[@KRITTIKAAURORA]

Times likes these We need to be "Unified", But today We "Divide"

[@laurentagainstheclouds]

I respect Michael so much that I'm getting to bed just to watch him the most comfortable I can be. he deserves all my attention.

[@thomasschmidt4193]

B. F. S I M P

[@hamimseam2591]

Thomas Schmidt michael’s an exception, he’s not a thot

[@caleblewis8169]

Better than math teachers

[@jfk9090]

@@thomasschmidt4193 reddit moment.

[@randomnpc445]

Legit did the same thing. I routinely eat snacks or meals while I watch videos, but opted out of doing that with this one so I could pay attention to it.

[@TurkishKS]

Easier 8 rule: Look at last three digits. If hundreds place is even, and last two digits are divisible by 8, entire number is divisible by 8. If hundreds place is odd, and last two digits are divisible by 4, but not 8, entire number is divisible by 8.

[@ShauriePvs]

Can we just say that if last 2 digits are divisible by 4 and the entire number is even, then it's divisible by 8? (Applying same logic as 6 divisibility)

[@hugebuffman3619]

​@@ShauriePvs I might be wrong since I've yet to graduate middle school, but i think that only applies to prime numbers because they have no common divisors and as such the least common multiple of them is their product, meaning that if the number is divisible by both of them then it is divisible by their product. The least common multiple of 2 and 3 is 6 because 2*3=6, the least common multiple of 2 and 4 is 4 because 2*2 = 4*1. As I said, my explanation might be wrong

[@volodyadykun6490]

@@ShauriePvs every divisible by 4 number is even, so entire number will be always as well

[@TurkishKS]

@@ShauriePvs As vova said, the entire number will be both even and divisible by 4 to even be considered as a candidate divisible by 8. It's just the hundreds place digit that you must consider, to decide whether or not you'd like the remaining 2-digit number to be divisible by 8 or not. If the hundreds digit is even, you need only check if the remaining 2-digit number is divisible by 8, to confirm the entire number is divisible by 8. If the hundreds position is odd, you want the remaining 2-digit number to be divisible by 4, but not 8, for the entire number to be confirmed as divisible by 8.

[@ShauriePvs]

@@TurkishKS ok thanks for correcting me

[@DemonXeron]

Here from Matts video! This is a great video!

[@sabersight908]

"GIANT PANDEMIC" Michael: hmmm i haven't uploaded in a long time lets make everyone's day better

[@caleblewis8169]

Micheal: I'm gonna do what's called a pro gamer move

[@ThorHC11]

@sw4gr1d by definition this IS a pandemic. Even if you don't think it's serious, it's still a pandemic because it is worldwide.

[@olivestamma]

By far the most amazing thing in this video is at 8:17 when he perfectly draws a check mark on another check mark

[@Sc0tcht4pe]

I feel like Michael is hiding something from us and tries to cover it up with all of this interesting stuff to distract us.

[@dangakun]

This is the onboarding video for new employees at the math factory

[@NoSlaying]

Me: *finally escapes online classes Michael:

[@ourochroma]

Division: easy tricks Number Seven: My Mom says I'm special

[@dayjay2011channel]

I stated watching micheal when i was 13 in middle school and here i am 18 and on break at work and my enthusiasm and love for his videos never died, I'm so freaking glad he hasn't lost his love for making videos

[@interestingperson7205]

I remember watching this when it came out. I didn't understand it back then but now after some algebra, and now calculus, This actually makes a lot of sense.

[@calvinwhite6219]

"COVID-19 is extremely viral and we should practice social distancing... Or should we???"

[@dhavalghone9398]

Hahaha classic Michael am i rite?

[@bluebaconjake405]

*big brain music starts

[@pinicius]

* cue Vsauce music * -- music stops -- * Michael looks serious at the camera * Yes! Yes, we should!

[@92jwiener]

Vsauce: Here in Miami, FL...

[@bear4304]

Yes

[@cantaskin04]

3:27 the subtlest nod to the memers I've ever seen

[@jeffireymurdock2073]

Didnt notice 🤣

[@Renteks-]

not a clue what this was talking about

[@viktor5918]

I´ve been practicing self isolation my whole life....

[@emrekaraman6877]

Gamer

[@nolongerusing7430]

same

[@gabor6259]

Introverts unite! Separately in our rooms. _(stolen comment)_

[@kryt7955]

the fact that he writes 8 by drawing 2 circles unsettles me

[@duchi882]

I came here with a Popcorn I came out with a Mathematics Degree

[@0bread286]

No one, Duchi: *a* popcorn

[@hachikiina]

only one

[@b0leg23]

Shouldn't you say "went out"?

[@saulo4302]

Also, popcorn with a capital "P", which implies it's either someone's name, or a place's name. You can't carry a place around -or can you?- , so I guess they watched with a friend?

[@jalapenopoggers8310]

Michael, I've been watching your videos for years now. Never before have I found someone who can explain things so well and clearly yet keep me hooked on any topic. I know this may not mean much in these crazy times but you cheer my day up at times and I appreciate you and your videos. Stay quizzacious out there!

[@rradrr]

“Ding Dong” should be the start up to every D!NG video, of course it should be said like this “Ding Dong, Michael here”.

[@ThatGuyCanmanNC]

That’s a ding dong moment

[@bluebaconjake405]

Its a modern take on the knock knock joke

[@rradrr]

Jake Johnson evolution 100

[@umkm2k]

I got legitimately excited when he finally got to 7. Nerd status: confirmed.

[@thepriestunknown3999]

15:38 for anyone in a hurry

[@funny_monke6]

An easier explanation for the 7 rule, more fitting to the other explanations: abc = 100a + 10b + c Rule is 10a + b + 5c \___,__/ This is the "add the rest" To get back to the original: 10(10a + b + 5c) - 49c ^ no effect ^ divisible by 7

[@whirpoolgalaxy7711]

QUICK MATHS

[@apersonontheinternet7607]

you learn divisibility rules at, like, 3rd or 4th grade, man. They won't even understand.

[@FunnyAnimatoFilms]

I feel like with the example in the video it'd just be faster to do the long division by hand.

[@bkshr1172]

This thing had been bothering me for almost 15 years now. Now i got the answer.

[@YT_Admin_]

Learn about congruence modulo You will get more satisfying answer

[@DeMooniC]

This is the first time even in my life im watching a pure math video not because of school but because I wanted to... WOW, Michael really is powerful lmao

[@JoniKauf]

10:18 When she says, my parents aren't home.

[@gumunduringigumundsson9344]

🤣👍

[@rjkzk]

0:00 her doorbell after 0.1354 seconds

[@JoniKauf]

JS K (*≧m≦*)

[@saulo4302]

@@rjkzk If "That Guy" can help me out please, I'm trying to learn more about the english language. Technically that's not more than one second, so should it be "0.1354 second"?

[@explosivemuffin795]

Michael: We are going to learn the divisibility rules Me, who had to do a song with the divisibility rules: I am 4 parallel universes ahead of you

[@James-rr6uh]

Wow it’s great to see Michael making a fun and educational video that can be enjoyed by children and adults alike. In these times positive learning is what we need most. Thanks man :)

[@subramanyannv9858]

The easier way to test for divisibility by 7 is to multiply last digit by 2 & subtracting from preceding digits. Eg. 36288: 3628-2*8=3612. 361-2*2=357. 35-2*7=21. So 36288 is divisible by 7.

[@aleksstake5168]

oh no he forgot his password again...

[@akul5400]

Oily black man.

[@2neutrino]

Thus

[@technoultimategaming2999]

Ikr. I'd say Vsauce fits really well

[@g.hmusicc]

Technoultimategaming yeah with an intro like “hEy vsauce michael here!”, that sounds cool.

[@whitetiger8115]

Omg ur right it should

[@Drozey710]

I agree however he doesn't seem like the type of guy to have time to upload..