How does the Euclidean Algorithm work?

Question

I just found this algorithm to compute the greatest common divisor in my lecture notes:

public static int gcd( int a, int b ) {
    while (b != 0) {
                 


        

Answer 1

They're equivalent. First thing to notice is that q in the second program is not used at all. The other difference is just iteration vs. recursion.

As to why it works, the Wikipedia page linked above is good. The first illustration in particular is effective to convey intuitively the "why", and the animation below then illustrates the "how".