This post is going to focus on a very simple concept, finding the GCD of two numbers. If you think this is too easy and we don't need a post on it, well you are probably right :D. You might even be knowing of efficient ways of finding the GCD (mostly used in competitive programming). But many of you may not be aware of the mathematics and proof behind how that method works. If that is the case, you are not alone. I was in the same boat for many years. I have used that 3 line GCD method many times in solving programming questions never thinking deeply about why it works. There is no issue in this. After all there is a good reason why abstraction is so popular. But I do believe that when you get a chance there is no harm in diving deep. You may get to learn a few things and as always be fascinated by what math has to offer even in the simplest of concepts. So lets begin... Context Now we all know one way at least of finding the GCD of two numbers. Find all the factors of both the n...