Find GCF or GCD using the Euclidean Algorithm (solutions, examples, videos, worksheets, games, activities)

Use the Euclidean algorithm to find a) gcd(12,18). b) gcd(111,201). c) gcd(1001, 1331). d) gcd(12345,54321). e) gcd(1000,5040) f) gcd(9888,6060). | Numerade

SOLVED:The extended Euclidean algorithm can be used to express gcd(a, b) as a linear combination with integer coefficients of the integers a and b . We set s0=1, s1=0, t0=0, and t1=1 and let sj=sj-2-qj-1 sj-1 and tj=tj-2-qj-1 tj-1 for j=2,3, …, n, where the qj are the quotients in the divisions used when the Euclidean algorithm finds gcd(a, b), as shown in the text. It can be shown (see [Ro 10]) that gcd(a, b)=sn a+tn b . The main advantage of the extended Euclidean algorithm is that it uses one