Euclidean algorithm

Okay kiddo, Euclidean algorithm is a way to find the biggest number that can divide two other numbers without leaving any remainder.

Let's imagine you have two big piles of blocks, one pile has 12 blocks and the other has 8 blocks. Now you want to divide both piles into smaller piles with the same number of blocks in each small pile, without having any blocks left over.

So you start with the biggest number, which is 12, and ask if it can be divided by 8. Well, it can't because 8 is smaller than 12, but 8 can go into 12 one time with 4 left over.

Now, instead of giving up, we use the leftover number 4, and ask if it can be divided by 8. No, it can't, but it can be divided by something smaller than it. 4 can be divided by 2 two times without leaving any blocks left over.

Now, we take that number 2 and ask if it can divide 8. Yes, it can! And we don't have any blocks left over.

So, the biggest number that can divide 12 and 8 without any leftover blocks is 4. Pretty cool, huh? This is what we call the Euclidean algorithm.