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.

       /**
        * Java method to calculate the greatest common divisor
        * @return the gcd of two integer
        */
       private static int gcd(int x, int y) {
           if(y == 0) {
               return x;
           }
           return gcd(y, x % y);
       }

2. c