The Largest Common Factor (LCF) for two positive integers n and m is the largest

Question

The Largest Common Factor (LCF) for two positive integers n and m is the largest integer that divides both n and m evenly. LCF(n, m) is at least one, and at most m, assuming that n greaterthanorequalto m. Over two thousand years ago, Euclid provided an efficient algorithm based on the observation that, when n mod mnotequalto 0, LCF(n, m) = LCF(m, n mod m). Use this fact to write two algorithms to find the LCF for two positive integers. The first version should compute the value iteratively, The second version should compute the value using recursion.

Explanation / Answer

Euclidean Algorithm for finding GCD(A,B) using iteration:

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