Problem

An alternative to the Euclidean algorithm uses subtraction rather than division to compu...

An alternative to the Euclidean algorithm uses subtraction rather than division to compute greatest common divisors. (After all, division is repeated subtraction.) It is based on the following lemma:

Lemma 4.8.3

If a b > 0, then gcd(a, b) = gcd(b, a b).

a. Prove Lemma 4.8.3.

b. Trace the execution of Algorithm 4.8.3 for A = 630 and B = 336.

c. Trace the execution of Algorithm 4.8.3 for A = 768 and B = 348.

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Solutions For Problems in Chapter 4.8