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

given that 'q' is never used, I don't see a difference between your plain iterative function, and the recursive iterative function... both do

gdc(first number, second number)
  as long as (second number > 0) {
      int remainder = first % second;
      gcd = try(second as first, remainder as second);
  }
}

Barring trying to apply this to non-integers, under which circumstances does this algorithm fail?

(also see http://en.wikipedia.org/wiki/Euclidean_algorithm for lots of detailed info)