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Greatest Common Divisors

1. Let a, b be positive integers, and write a = qb + r, where q, r are Elements of Z and
0 (= or)< r < b. Suppose that d = gcd(a, b).
a) If r = 0 show that d = b.
b) If r > 0 show that d = gcd(b, r).

4. Use Problem 1 to find:
a) gcd(100; 3);
b) gcd(100; 82).

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Greatest Common Divisors are investigated.

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