I explain the Euclidean Algorithm, give an example, and then show why the algorithm works. Outline: Algorithm (0:40) Example - Find gcd of 34 and 55 (2:29) Why it Works (3:58)
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@praveenanookala44574 жыл бұрын
Ma'am, this has to be the best mathematics video on KZbin that I've seen. So concise and immensely explanatory!!! Thank you very much! Subscribed!
@glitch3dout6 жыл бұрын
This is the best video I could find on the internet that explains the Euclidean Algorithm so concisely and comprehensibly. Thanks a bunch!
@manishsahamanishsaha12683 жыл бұрын
Y'r right !
@episkefilm8153 Жыл бұрын
you just something I've used 20 minutes struggling to even begin to understand, and explained it in such a simple way in like 5 minutes. Wish more math teachers were like you
@octavios80814 жыл бұрын
The theorem proven at the end was what I was looking for, thank you!!
@Pandafist30005 жыл бұрын
Thank you for an excellent proof of the Euclidean algorithm. Exceptionally clear and thorough.
@peteryongzhong55166 жыл бұрын
This is so well done. Why isn't this the top result when I search on google. Literally so much clearer than the textbook!!!
@fixer25082 жыл бұрын
I had been trying to decipher someone else's post on this for hours on end with no luck. Watching this video completely cleared it up for me! Thanks!
@shauryanagpal18484 жыл бұрын
I am actually in 10th standard and I was wondering why does the Euclid's Algorithm works ? And here is the answer thank you ma'am
@user-qd4dg3xv3l4 ай бұрын
Same here bro
@hannahpatel71977 жыл бұрын
Thank you so much for your videos. Your explanations are so clear and concise - excellent maths brain!
@tiandao1chouqin4 жыл бұрын
Very nice and clear explanation. Thanks. Would love to see more videos from you
@Andrey-ny2dv6 жыл бұрын
I rarely leave comments but I just wanted to tell you that this video is full and brilliant.
@lucianocao87874 жыл бұрын
I was struggling understanding the proof and I finally got the intuition thanks to this video.
@gonzalochristobal4 жыл бұрын
great explanation thank you! it would be great if you can find some time to make more videos like this :) but thanks a lot for the ones that you already made!
@davidemasi__3 жыл бұрын
You made this algorithm very easy to understand, thank you very much for this great video
@greyshinobi697 жыл бұрын
nicely explained and in depth.Thank you!
@naif2774 жыл бұрын
Very well explained, thank you!
@kwokpinglau24005 жыл бұрын
Thank you so much, you proof the theorem clearly.
@mysia84373 жыл бұрын
I watched on 4 different channels and i understand that only you did. So thank u.
@MarziyeFatemi-xg2ty7 ай бұрын
Such a great teacher you are! Thanks!
@raginibhayana83053 жыл бұрын
Thank you so much for making this video
@valeriereid233711 ай бұрын
Thanks very much for making this easy to understand.
@abd-elrahmanmohamed98396 жыл бұрын
Well explained . Thanks a lot !
@rajendramisir35305 жыл бұрын
Well organized proof. QED. Carl Gauss: Number theory is the Queen of Mathematics.
@kunalsinghgusain20704 жыл бұрын
What about the king?
@adityakrishna114 жыл бұрын
great proof thank you so much for this!
@michaelbachmann457 Жыл бұрын
very good proof explanation
@m_sh22402 жыл бұрын
thank you so much for doing this🎉
@RoyalGun-9mm Жыл бұрын
short and informative.. perfect.
@srikantht24034 жыл бұрын
Thank you
@SathvickSatish6 жыл бұрын
Very well done presentation! You should be really popular!
@seal01183 жыл бұрын
wow, very intuitive, thanks
@ziedbrahmi4812 Жыл бұрын
a great video, thank you ! (LIKED IT AND SUBSCRIBED)
@rishabhpandey38226 жыл бұрын
very nicely done👍
@josephlai77373 жыл бұрын
Thank you so much!
@user-ye7yu2zc4t2 жыл бұрын
One of the best tutorial I have ever found 🔥
@silicon9794 Жыл бұрын
Excellent explanation, understood clearly 😃
@yeah50372 жыл бұрын
4:31 actually the theorem was proved by using the Euclidean Algorithm, while Euclidean Algorithm is proved using strong induction over the variable a here
@edisonyin97113 жыл бұрын
Thank you so much, that helps!!
@ruthwik87724 жыл бұрын
Hopefully great video for the proof of this algorithm
@aksenchukaleksandr327310 ай бұрын
thank you. very helpful
@TamNguyen-yk9mn3 жыл бұрын
It always amaze me to think that ones upon a time someone thought of this.
@cubingtubing81723 жыл бұрын
Yeah, same for me. Considering how much humanity has grown in the last century, we tend to think that the humans before were apes
@trendytrenessh4625 жыл бұрын
Thanks a lot this really helped! :)
@DEEPAKKUMAR-oo1vv3 жыл бұрын
Thank you so much.
@krishshah39744 жыл бұрын
talk about perfection!
@pulse58635 жыл бұрын
absolutely amazing thank you so much ! you are awsome.
@abhinavraut30993 жыл бұрын
Thank you!
@math_lover52923 жыл бұрын
Really this video has helped me a lot......never wondered such beautiful stuff could be arrived by just using these simple steps........school teachers never make us fall in love with maths by providing such beautiful proofs.... Thanks a lot mam..... ❤️🧡💛💚💙💜🤎🤍_from india.....
@thechaoslp20473 жыл бұрын
beautiful. thank you.
@AsBi13 жыл бұрын
Very helpful.
@thachpham85972 жыл бұрын
Thank you very much
@aneimabui97183 жыл бұрын
Thanks 🙏 for helping me
@mcat01833 жыл бұрын
Thank you so much :)
@samarthjain52953 жыл бұрын
Finally i understood this..... thanx a lot😁
@HiHi-iu8gf3 жыл бұрын
best explanation i've found so far, but brain still kinda fried lol
@edwinshelly9933 жыл бұрын
Thanks a ton!
@kunalsinghgusain20704 жыл бұрын
You got my sub 👍 and a thanks.
@mwsedits4 жыл бұрын
Nice way to explain. May Allah bless u a sound health. Also voice is also great. Which is easily understandable.. Keep students make there issues clarify on priority. Also make more math videos on m phil topics plz.
@gladyouseen81605 жыл бұрын
Wonderful
@mr.shanegao3 жыл бұрын
Outline: Algorithm (0:40) Example - Find gcd of 34 and 55 (2:29) Why it Works (3:58)
@calvin28889 ай бұрын
Excellent.
@mjjeon22926 жыл бұрын
If you mention your other video while explaining, please leave a link.
@ashutoshniwal3 жыл бұрын
Wow you have explained it very nicely, but your proof doesn't still explains that why the common divisor would be the "greatest" and not any common divisor? How to prove that d=e?
@willjohnston29597 ай бұрын
The proof shows that the set of numbers of the form d (that divide a, b, and r) and the set of numbers of the form e (that divide a, b, and r) exactly match. These are finite sets, and they have a largest element, so those largest elements must match.
@kunalkashyap99043 жыл бұрын
Thank you sir :) I have studied many topics of Vidya Guru channel as well. They also use updated exam relevant content.
@damandeepsingh85423 жыл бұрын
Pls make a video on hcf and lcm of fractions with their proof
@wpajunior6 жыл бұрын
Good! Thank you
@user-ye7yu2zc4t2 жыл бұрын
Thank you so much maam
@renjitharejikumar16196 жыл бұрын
Thank u sooo much maam👍
@navyatayi69567 жыл бұрын
this is really well done! please keep making videos of more math proofs...especially on topics like calculus...please..this video is very clear to understand...and thank you for this video
@marvhartigan36774 жыл бұрын
Good to see there are people like you actually interested and not just blindly applying formulas.
@manishsahamanishsaha12683 жыл бұрын
you shut ur mouth up !
@minatirout32865 жыл бұрын
Thanks a lot
@peterren54094 жыл бұрын
At 3:44, I think the last equation should be 2 = 1*(2) + 0 instead of 2 = 2*(1) + 0
@praveenanookala44574 жыл бұрын
+Peter Ren That's right.
@aryamankarde4733 жыл бұрын
Which country are you from ma'am ? I want to meet you, you are such a wonderful teacher.
@damandeepsingh85423 жыл бұрын
Very good
@TheBSpaZZ5 жыл бұрын
What a wonderful Video. I applaud you. I suggest you include a "Thanks you" at the end, gives the video closure when playing full screen.
@zahra-hrm3 жыл бұрын
Thank u 😊
@gogoat24124 жыл бұрын
3:30 you made the fibonacci sequence!!
@kushalpawar95714 жыл бұрын
Wow mind blown
@cubingtubing81723 жыл бұрын
So the common divisors are the same, but why greatest? Is this some anecdote that has been found over centuries or is there proof available for it?
@dogamertaydogan28035 жыл бұрын
thanks
@coctaildz53883 жыл бұрын
i did not understand the last conclusion , can any one explain it to me from 08:13
@davidjiang79294 жыл бұрын
Hi there, I liked your explanation here. Very concise. However, I am missing a piece of the puzzle. So far, we proved 1) if d is a factor a and b, then d divides r 2) if d is a factor of b and r, then d divides a But how do we imply from these 2 statements that d is the gcd? i.e. we only proved that d is a factor of the 3 items, but not the greatest divisor? Thanks!
@mountainsunset8164 жыл бұрын
Exactly, I am also confused about this.
@mountainsunset8164 жыл бұрын
Just got it. Since d can be any factor, so it can also be the greatest common divisor.
@kevinmartincossiolozano82453 жыл бұрын
I think it helps to understand that it works for ANY divisor.
@thechaoslp20473 жыл бұрын
The set of common divisors between a,b is identical to the set of common divisors of b,r The greatest common divisor is simply the greatest number of the set of common divisors. If the two sets are the same, the greatest member of the set must also be the same for both. So the gcd is the same for both pairs.
@davidjiang79293 жыл бұрын
@@thechaoslp2047 I think this is what I was missing. I was too hung up on the fact that we only got common divisors for both sets, and did not prove that the fact that the common divisors are the greatest common divisor.
@rameshchandra16966 жыл бұрын
Neat.
@harivatsaparameshwaran41746 жыл бұрын
I mean tho its fairly obvious that a multiple subtracted from a greater multiple is still a multiple, don't u have to prove that a-bq is also divisible by d?
@biocuts4 жыл бұрын
no, because (a-bq)/d => a/d - (b/d)q, and that's an integer since a/d and b/d are integers, meaning it is divisible.
@adityasoni69664 жыл бұрын
To understand completely, why gcd(a,b)=gcd(b,r) , first try to understand why gcd(a,b) !=gcd(a,r).
@champion55455 ай бұрын
Wait, pause. How does d being a divisor of b suddenly make d being a divisor of bq? How did you reach that conclusion?
@lbmath54415 ай бұрын
If d is a divisor of b, then it would have to be a divisor of any multiple of b. And bq is a multiple of b. For example, if 6 divides 12 (letting d = 6 and b = 12), then 6 divides 12(3) (letting q = 3). More generally, once you know 6 "goes into" 12, you know that 6 "goes into" any multiple of 12. Once you know d "goes into" b, you know that d "goes into" b times any other whole number, so it "goes into" b times q.
@luciuspertis56725 жыл бұрын
THIS IS SO TO THE POINT .............. HATSsssOFF
@AjayKumar-fb3gx6 жыл бұрын
i lost you after you said e | a at 8:04. how did you get to the 'iff' statement ?
@abuabdullah98784 жыл бұрын
It's clearer if we write it like this: Forward: (d|a AND d|b) -> (d|r AND d|b). Note, 'd' is any common divisor of 'a' and 'b'. Backward: (e|b AND e|r) -> (e|a AND e|b). Here, 'e' is any common divisor of 'b' and 'r'. So, any common divisor 'a' and 'b' is a common divisor of 'r' and 'b'. Also, any common divisor of 'b' and 'r' is a common divisor of 'a' and 'b'. Therefore, (a, b) and (b, r) share the same set of common divisors. Thus, the gcd(a, b) = gcd(b, r) as needed.
@mountainsunset8164 жыл бұрын
@@abuabdullah9878 Dude, how can you tell that the shared common divisor is the gcd? I did not quite get your last sentence and the last step in the video.
@adam-jm1gq4 жыл бұрын
@@mountainsunset816 the way I've figured it, is we now know that the 2 sets are identical. So d and e and f and g and so on for however many iterations, all are common divisors in an identical set. So d for example could be any divisor in the set and e could also be any divisor and so on. Say for e.g you do a lot of iterations and get an answer of 1233 = 3(411) +0 You have now reached the point where there is no remainder left. We now know that any common divisor of 1233 and 411 is also any common divisor of the original a and b (in this case a=7398 and b=2877) So if we want to know the greatest or largest common divisor of 7398 and 2877, then simply find the gcf of 1233 and 411. Well, there is no remainder and 411×3 = 1233 as figured out by the iterations. So 411 must be the gcf(1233,411). Thus it is the gcf(7398,2877). Please feel free to correct me if I'm wrong, I just thought I'd learn some uni maths in lockdown before I start uni, so I could be completely and utterly incorrect
@andrewkarem58744 жыл бұрын
@@@adam-jm1gq @Mountain Sunset: You're both on the right track. As Abu indicated, the shown steps demonstrate that (a, b) and (b, r) share the same set of common divisors -- and so do any of the (a,b,r)-type combinations throughout the sequence of steps. So (b, r) and (r, r_1) share the same set of common factors, as do (r,r_1) and (r_1,r_2)...all the way down to (r_i-1,r_i) sharing the same set of common factors as (r_i,0). But the greatest common factor of r_i and 0 is simply r_i! So you can think of this value propagating all the way back up through the sequence, since any LARGER divisor common to (a,b) would also be common to (b,r), which would be common to (r, r_1), ...all the way down to (r_i,0).
@praveenanookala44573 жыл бұрын
@@andrewkarem5874 Oh, you made it so clear! Thank you!
@ankitthakurankit47642 жыл бұрын
3:30 i think gcd(55,34) is 2 as ri here is 2
@legendsplayground7017Ай бұрын
Great job, it's really clear, thanks for that :) Jesus bless ❤
@abdullaha21085 ай бұрын
I dont understood one point that is, how d|a, d|b implies that d|a-bq. Please any buddy explain me.
@lbmath54415 ай бұрын
Anytime you have d "dividing" a number (i.e. d divides b), then it divides a multiple of that number (so d divides bq). For example, if 6 divides 12, then 6 divides 24, and 36, and 48, etc. So if d|b, then d|bq. Furthermore, if d divides two different numbers, a and bq, then it divides their sum or difference, since if it's a factor of both, you can "factor it out" of the expression. So, if d|a and d|b, then d also divides bq, and therefore it divides a - bq.
@abdullaha21085 ай бұрын
Thank you buddy. Nice explanation. @@lbmath5441
@hansvandenbogert89926 жыл бұрын
Should the last line in the example not be "2=1(2) +0" ?
@simranmulchandani61906 жыл бұрын
Hans van den Bogert Yes definately
@user-ly9vg7bp6l5 жыл бұрын
日本語の教科書よりわかりやすい
@user-od2ox5we4b3 жыл бұрын
ALL I CAME FOR WAS IN 6.26 AND DIDN'T UNDERSTAND IT .... DAMM IT