What are the greatest common divisors of these pairs of integers?a) 37 · 53 ·73, 211 · 35·59________________b) 11 · 13· 17, 29 · 37 · 55 · 73________________c) 2331, 2317________________d) 41 ·43 · 53, 41 · 43 · 53________________e) 313 · 517, 212 · 721________________f) 1111, 0
Solution:-Step1Given thatWe have to find what are the greatest common divisors of these pairs of integersStep2a) 37 · 53 ·73, 211 · 35·59Definition: - The greatest common divisor, sometimes also called the highest common divisor of two positive integers c and d are the largest divisor common to c and d.The positive common divisor of two number isSo, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are .Step3b) 11 · 13· 17, 29 · 37 · 55 · 73The positive common divisor of two number is 1.So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are .Step4c) 2331, 2317The positive common divisor of two number is So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are .Step5d) 41 ·43 · 53, 41 · 43 · 53The positive common divisor of two number is So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are Step6e) 313 · 517, 212 · 721The positive common divisor of two number is 1So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are 1.Step7f) 1111, 0The positive common divisor of two number is So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are 1111.
