Use the Euclidean algorithm to finda) gcd(12, 18).________________b) gcd(111, 201).________________c) gcd(1001, 1331).________________d) gcd( 12345, 54321).________________e) gcd(1000, 5040).________________f) gcd(9888, 6060).
Solution:-Step1Given thatWe have to use the Euclidean algorithm to find gcd.Step2a) gcd(12, 18)By using Euclidean algorithmAs 6 is the last nonzero remainder.Therefore, gcd(12, 18) is 6.Step3b) gcd(111, 201)By using Euclidean algorithmAs 3 is the last nonzero remainder.Therefore, gcd(111, 201) is 3.Step4c) gcd(1001, 1331)By using Euclidean algorithmAs 11 is the last nonzero remainder.Therefore, gcd(1001, 1331) is 11.Step5d) gcd( 12345, 54321)By using Euclidean algorithmAs 3 is the last nonzero remainder.Therefore, gcd( 12345, 54321) is 3.Step6e) gcd(1000, 5040)By using Euclidean algorithmAs 40 is the last nonzero remainder.Therefore, gcd(1000, 5040) is 40.Step7f) gcd(9888, 6060)By using Euclidean algorithmAs 12 is the last nonzero remainder.Therefore, gcd(9888, 6060) is 12.
