Math if fun

1. Greatest Common Divisor, gcd(a, b)
   • If b|a then gcd(a, b) = b.
   • If a = bt + r, for integers t and r, then gcd(a, b) = gcd(b, r).
     • Indeed, every common divisor of a and b also divides r. Thus gcd(a, b) divides r. But, of course,gcd(a, b)|b. Therefore, gcd(a, b) is a common divisor of b and r and hence gcd(a, b) ≤ gcd(b, r). The reverse is also true because every divisor of b and r also divides a.

        1 /**
        2  * Java method to calculate the greatest common divisor
        3  * @return the gcd of two integer
        4  */
        5 private static int gcd(int x, int y) {
        6     if(y == 0) {
        7         return x;
        8     }
        9     return gcd(y, x % y);
       10 }

2. c