Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Please explain me the Euclidean Algorithm. Help appreciated.

See more answers at
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly


Get your free account and access expert answers to this and thousands of other questions

First step, look at an example. I'll color things to make it easy to see what I'm doing.
Okay - I follow.
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, \(\gcd(572,165)=11.\)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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.
So the point is that we must repeat it again and again till we get the remainder 0? That does make sense.
May I have a practice problem?
Try it out on \(a=342\) and \(b=295\).
One more thing, make sure \(0\leq r
@KingGeorge - wonderful explanation! :)
I wish that the Chrome Aw Snap didn't exist.
OMG I never knew it's called euclidean algorithm. I love this method. lol
\[342= 295\cdot 1 + 47 \]\[295 = 47 \cdot 6+13 \]\[47 = 13\cdot 3+8 \]\[13 = 8\cdot 1 + 5 \]\[8 = 5 \cdot 1 + 3 \]\[5 = 3 \cdot 1 + 2 \]\[ 3 = 2 \cdot 1 + 1\]\[2 = 1 \cdot 2 + 0 \]
So, they are co-prime!
Thank you :)
Let me return back to that CRT question. Okay.
You're welcome. If you want a proof of the algorithm, I could probably type that up as well.
Haha no :P

Not the answer you are looking for?

Search for more explanations.

Ask your own question