a) Show that if a1, a2, . . . , an are positive integers, then gcd(a1, a2,

Question:

a) Show that if a1, a2, . . . , an are positive integers, then gcd(a1, a2, . . . , an−1, an) = gcd(a1, a2, . . . , an−2, gcd(an−1, an)).
b) Use part (a), together with the Euclidean algorithm, to develop a recursive algorithm for computing the greatest common divisor of a set of n positive integers.