Reference no: EM131570500

Question: Show that if a and b are positive integers with a ≥ b, then gcd(a, b) = a if a = b, gcd(a, b) = 2 gcd(a/2, b/2) if a and b are even, gcd(a, b) = gcd(a/2, b) if a is even and b is odd, and gcd(a, b) = gcd(a - b, b) if both a and b are odd.

b) Explain how to use (a) to construct an algorithm for computing the greatest common divisor of two positive integers that uses only comparisons, subtractions, and shifts of binary expansions, without using any divisions

c) Find gcd(1202, 4848) using this algorithm.