GCD: problems of the algorithm implementing directly the definition

How many times do we execute the loop in the previous algorithm?

• best case: 1 time, when x divides y or vice-versa
  E.g.,  gcd(500, 1000)

• worst case: min(x, y) times, when gcd(x, y) = 1
  Ex . gcd(500, 1001)

Hence, the previous algorithm behaves bad when x and y are big and gcd(x, y) is small.