Euclid algorithm

Exercise 5. Euclid's algorithm for computing the greatest common divisor for positive integers A 2 B can be described by the following recursive pseudocode: GCD(A, B): if B divides A then return B else return GCD(B, A mod B) Prove that this algorithm takes at most 2n iterations when run on n-bit integers A2 B A Hint: Let At Bt be the arguments to the GCD function at the th iteration, so that A and B B. What can you say about the decrease of At, as a function of t