Extended Euclidean Algorithm Example

In this video I show how to run the extended Euclidean algorithm to calculate a GCD and also find the integer values guaranteed to exist by Bezout's theorem.

[@craigtyle]

Super clear - the point about treating the underlined numbers as variables was key.

[@user-hh6lb4rx1c]

Dude taught in 15 minutes what my boolean algebra teacher couldn't in a week.

[@billygraham5589]

Isn't it the truth! ; ) lol And they say those that can't do, teach... not true. Those that can't do, can't teach, and those that can teach, we are lucky to be able to learn from them, because there are so many that can't teach, and can't do... a miserable lot they are.

[@bakangsbakho8852]

Euclid and Bezout were on drugs that day

[@panos13ole]

lmao

[@rayyisbaeee]

@@panos13ole true

[@KP-sg5ni]

lol

[@epicm999]

Lol

[@isiraadithya]

facts

[@elChico-TV]

Best and simplest explanation on KZbin . Thanks

[@nayefalsalahat9928]

ds

[@kevinramdass8608]

Treating the underlined numbers as variables was a game changer...Thank you so much @John Bowers

[@michellemason8503]

Showing the underlining of the numbers really was the missing link for my brain to understand this! Thank you!

[@ethann8827]

The perfect math video doesn’t exi-

[@stevewest6133]

This is the best video I've seen on the extended Euclidean. The pointer at 9:50- to treat the number as if they were variables- is a critical step for people learning this for the first time. A lot of other videos speed through this critical step.

[@jimmyjay5825]

Thank you for this video! Been trying to get this right for quite some time and have watched several other lessons. When you said to treat the numbers as variables was really when it became clear to me! Well done! You really saved me from failing my exam!

[@52cent]

This guy is the best explanator of such a complicated thing. Everything in simple words and step by step. THANKS

[@BittiKit]

Wonderful explanation. I watched several videos, and this was the only one that really made me understand the substitution process. Thanks!

[@wrx1th873]

the greatest video of all time. watched 10 different videos on the same topic but they all have 1 thing in common, they dont tell you the real deal, they just assume you already know that 1 thing so they quickly brush it off. The whole underline as a variable thing is a game changer and what made me understand. Thank you.

[@user-sr1bv1tu5e]

I missed a day in a prep course for the university and that was the subject. you made it so clear what they were talking about on the next day, thank you so much!!

[@ya00278]

I'm so lucky to find your video! It's clear and easy to understand. I'm struggling in my class. your video just saved my life!

[@4everThoughtful]

This is an absolutely excellent explanation for Bezout's theorem! Thank you!

[@abdelrahmanm.6215]

By far the best explanation iv seen on here, thank you so much John.

[@dugannash9109]

GREAT explanation. As others have noted, treating the numbers as variables is what ultimately unlocked this for me. It's so unlike anything I've done previously in my limited math experience, I could not tell what was happening until this video made it clear. Thanks a lot!

[@valentinenyagah5513]

At first I did not understand what my lecturer taught me in class but now I am happy to say i'll ace that exam....T hank you so much

[@angieCity90]

This was such a wonderful explanation. Straight to the point. I dig it

[@ajubenjamin1741]

Excellent method John. I have watched many videos about it. But this is fantastic . Thanks

[@SOMESHKHANDELIA]

This is the most beautifully explained video on this topic. Thank you so much!

[@slypete]

Thank you, this is the best video on extended Euclidean!

[@randomfr0g]

This is the best and most clear explaination I have ever seen. Thank you so much.

[@kristenwiley8869]

This was so much easier to understand than my textbook. Thanks a million!

[@johnbowers5447]

Great to hear!

[@creatorofimages7925]

Imagine a video, that is not intended to show, how to calculate the private exponent d in RSA with the extended euclidean algorithm, doing the best job of providing a step by step solution, with no holes or skips in it. Really good work! Your video is better than any RSA private exponent calculation video for understanding how the retreive d.

[@simpleTheMister]

that's exactly why im here damn

[@marveljoseph7096]

This was an amazing learning video. Thank you so much for making it clear and concise!

[@LuisHernandez-if3dc]

The absolute bestest explanation I could find for this, THANK YOU!!

[@illyias]

Absolutely phenomenal explanation, goes over every little detail so you can't possibly feel lost at any one step. Couldn't for the life of me figure it out with the textbook or the other weird videos where they use a table and formulas that seemingly come out of nowhere, but this made it abundantly easy to understand. One watch and I could execute it flawlessly :)

[@SahilSingh-yw9mg]

Thanks! was stuck at this Algorithm for quite long, you explained it very well in just a few minutes.

[@justinlangley1056]

It works really well and the video was really well done! Having grown accustomed to a lot of algebra, calculus, trig, etc. its hard to start treating numbers like variables, but that made it click for me. However, I don't feel like the simplifying aspect was explained as well as it could have been, which is an extension of what I mentioned in the previous sentence. To clear things up: After each substitution, in order to simplify, distribute the co-efficient (if we're still thinking in terms of variables) to the lower value in each term. If it confuses you, just put both in parentheses, distribute to the smaller value, and re-write in ascending order on a new line. Also, yes, you need to simplify after each substitution, its too easy to lose track of where to distribute, and you'll probably mangle where you put your parentheses causing you to distribute improperly. Following this, we'll properly build up to the input values we used to compute our GCD originally. You should be able to simplify to a pair of numbers every time that make sense for your next substitution. If you don't follow this you'll probably get a garbage answer from making a mistake when simplifying. You can follow in the example below how its done. Example: Find s and t, where: 240s + 46t = gcd(240, 46) // Perform our GCD calculations gcd(240, 46) 240 = 46(5) + 10 46 = 10(4) + 6 10 = 6(1) + 4 6 = 4(1) + 2 4 = 2(2) + 0 // Re-writing according to the video (numbered for referencing): Equation 3: 240 - 46(5) = 10 Equation 2: 46 - 10(4) = 6 Equation 1: 10 - 6(1) = 4 Equation 0: 6 - 4(1) = 2

[@sherlokholmes7865]

Was a challenge to find a video or an article that would explain this algorithm in simple terms. Thank you!

[@calculusbitch3577]

Had been confused my entire life with all these backward substitutionS. Thank you so much for this vid! It helped alot!

[@kokoraiado5409]

One of the best videos related to the topic, thank you sir.

[@tardigrade2244]

Awesome video! The way you explained the methods are very precise and easy to understand, kudos to you. Thanks a bunch, you are making the world a better place! Cheers

[@johnbowers5447]

Glad it helped! Thanks for watching.

[@hagenfarrell]

My professor was speed running this algorithm in class, we covered it in like 10 mins. Thank you for the thorough explanation!

[@sevmone]

You taught me in 15 minutes, while my discrete professor couldn't even teach me this in a whole semester !!!!!!

[@lazarstojanovic2538]

Amazing video!! Clear, straight forward, and quick and I actually know what I'm doing now.

[@DRTBerg]

Thank you for providing this excellent explanation on how to use the extended Euclidian algorithm!

[@r3dbag]

The best explanation I've seen so far.

[@seismicdna]

this video is awesome. makes the process completely understandable. thanks!

[@salmatasbahji4992]

absolutely great. it is amazing how great you explained that. GREAT WORK

[@jacobnichols2182]

Very good! Much easier than the formal explanation!!

[@Sangu_sss]

Thanks to you, many questions have been solved. Even though it's been a long time, you've been a good help.

[@0jas.]

This was a great explanation. I don't think any other teacher tells you to treat those underlined numbers as variables. That was pretty helpful.

[@4everThoughtful]

Hey, it's my first time hearing that ALSO and I'm a teacher!! 😌😌 I'm going to being using his techniques! He's an awesome teacher

[@user-ri2tx7bd7u]

thank you so much! I literally spent so much time trying to figure out my homework problem but now through your video, I learned how to complete problems like these!

[@just_bucket]

It's a shame we can't mark videos as the best solutions the same way we can do it on forums. This is definitely the best explanation on this topic.

[@elaine3867]

right

[@saurabhsharma359]

Thank you so much sir i watched multiple videos but everything was complicated and now this is my last video i don't need to watch anything else again thank you sir

[@OrenjiArms]

thank you, this part was super confusing but it makes so much more sense now

[@dhanaarvina142]

Thank you so much, John! it's so easy to understand

[@sinbadgmail]

one of the best math video i have seen in long time. thank you!

[@johnbowers5447]

Glad it was helpful!

[@fayzazzahrar]

very clear! been struggling with a problem like this and found your video!

[@johnbowers5447]

Glad it helped!

[@soumyadeeproy6611]

Made super duper clear,thanks for creating such good contents

[@Dmccumsey]

This has finally made sense, THANK YOU so much!! 🙏

[@shg__]

Great explanation, very much appreciated!

[@Killernochance]

This was phenomenal! Thank you!

[@cmrdecc6516]

Thanks a ton. God bless you, your family and country :)

[@hifriend783]

Wow! I was struggling so much with the intuition and this finally made things click.

[@hx4zx]

You explained it absolutely on point! Thank you!

[@colebaty1407]

Excellent breakdown! Thank you!

[@tomseo181]

Thank you for the clear and concise explanation.

[@jameskunstle1674]

I have a final tomorrow and this just taught me so much- thank you!

[@bjornolsson9103]

This was super clear, thank you for this!

[@ea1766]

Just brilliant, the variables was a game changer!

[@vishnughuge7690]

i took help of many videos but they were out of my understanding. this video explained me very nicely thanks so much

[@ButtKraken01]

It all makes sense now. Thank you so much!

[@lunatunny7594]

this got me through my month-long class in like, a few days. Sooo good goddamn

[@andrewbrenner9375]

Beautifully Explained. Thank you.

[@sadeemshehri2748]

you made it so so easy! I have an exam tomorrow and I didn't think I would have time to understand it (since it looked so complicated) Thank you!

[@johnbowers5447]

Glad it helped!

[@saurabhshinde1855]

The badass big rule nailed it 👌. Best explaination.. thank you so much

[@uladasplay5242]

Fantastic, very helpful video!

[@enquiem3051]

Very clean and understandable. Thank you !

[@KingofArmageddon20]

damn! so clear and straight to the point!!! thank you for this video!!

[@ShaolinMonkster]

Underline trick was amazing. Everything cleared out. I'd hope teachers like you [=that make thigns easy , and not teach jargon] had the seat of the teacher and not what is right now on my University.....

[@harry-fl6tf]

Brilliant job Professor!

[@rahulmaan2862]

You made it so simple! Thanks a lot!

[@kaiszer3921]

This is a perfect explanation, thank yoi very much!

[@nkechiakinwale5081]

Really easy to follow and understand, thanks so much

[@shai0123]

very nicely put and clear video. thanks!

[@MariiaKlochko]

thanks a mill! very well explained

[@damagecontrol7]

What a legend! Best explanation.

[@abhishektanwar8070]

Really good explanation. Thanks a lot from India.

[@jamieghoorbin4526]

Best explanation I've watched on YT 🕺🏿 Thanks 🙂

[@johnbowers5447]

Glad you think so!

[@shrouqmakk7676]

I asked my friends and watched so Many videos on youtube and still did not get it but thanks to u I get it now. thaankssss

[@salmakishk9759]

Thank you so much for your help!!

[@TheOscarJB]

It is easy to understand from zero, thank you so much

[@samsunnahar9175]

Thanks a lot for excellent explanation!!!

[@brockobama257]

Found another underrated golden channel

[@_Ahmed_15]

Best method of solving this. Every other video makes this so complicated.

[@footsoldier12x]

Incredible explanation. Way better than Zybooks.

[@tusharbhatt8257]

the best explanation !!

[@schoenwettersl]

I LOVE YOU!!!! 🤝 this was great

[@miclaszlo8420]

Great video, very helpful!

[@rongliao9255]

Great tutorial! Thanks a lot Master Teacher!

[@irvingrivas2985]

Great explanation, ty!

[@Cheems_on_Toast]

Great video, thanks!

[@lynettemojica6503]

I was having trouble with the back substitution but this helps, thanks.

[@m.k.m3826]

Thank you so much for this video. It saved me a question!

[@sammie1824]

thank you - this couldn't have been clearer!!!

[@insi6358]

the only egcd algorithm video that actually explains how to do it

[@muratylmaz1448]

Thanks, it helped me so much :)