Correctness

Why does this work?

• Termination is trivial, because the second argument is always decreasing by at least 1 and the process terminates when it reaches zero.
• Need to show .
  • First, note that any number that divides both a and b also divides .
  • Then, note that any number that divides both b and also divides a.

    

  • This implies that the largest such divisor of one pair must be equal to the largest of the other pair.