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ParthKohli
Group Title
Please explain me the Euclidean Algorithm.
Help appreciated.
 2 years ago
 2 years ago
ParthKohli Group Title
Please explain me the Euclidean Algorithm. Help appreciated.
 2 years ago
 2 years ago

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KingGeorge Group TitleBest ResponseYou've already chosen the best response.6
First step, look at an example. I'll color things to make it easy to see what I'm doing.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Okay  I follow.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.6
Look at \(a=572\) and \(b=165\). The euclidean algorithm will give us the gcd of these two numbers. Here's how you would find it \[572=\color{red}{165}\cdot3+\color{green}{77}\]\[\color{red}{165}=\color{green}{77}\cdot2+\color{blue}{11}\]\[\color{green}{77}=\color{blue}{11}\cdot7+0\]Now that that last number is 0, look at the remainder above it. In this case, that's 11. Hence, \(\gcd(572,165)=11.\)
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.6
The last number in each of those lines is called the "remainder" and the black numbers (3,2,7) are the quotients. In general, given any two numbers \(a,b\), they can be written as \[a=b\cdot q +r\]where q=quotient and r=remainder.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
So the point is that we must repeat it again and again till we get the remainder 0? That does make sense.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
May I have a practice problem?
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.6
Try it out on \(a=342\) and \(b=295\).
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.6
One more thing, make sure \(0\leq r<b\) in the equation \(a=b\cdot q+r\).
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
@KingGeorge  wonderful explanation! :)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
I wish that the Chrome Aw Snap didn't exist.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
OMG I never knew it's called euclidean algorithm. I love this method. lol
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
\[342= 295\cdot 1 + 47 \]\[295 = 47 \cdot 6+13 \]\[47 = 13\cdot 3+8 \]\[13 = 8\cdot 1 + 5 \]\[8 = 5 \cdot 1 + 3 \]\[5 = 3 \cdot 1 + 2 \]\[ 3 = 2 \cdot 1 + 1\]\[2 = 1 \cdot 2 + 0 \]
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
So, they are coprime!
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Thank you :)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Let me return back to that CRT question. Okay.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.6
You're welcome. If you want a proof of the algorithm, I could probably type that up as well.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Haha no :P
 2 years ago
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