GCD and coprimality of 51 and 91

Statement

Compute $\gcd(51,91)$ and decide whether the two numbers are coprime.

Solution

Factor them: $51 = 3\cdot 17, \qquad 91 = 7\cdot 13.$ They share no prime factor, so $\gcd(51,91) = \boxed{1},$ and the two numbers are coprime (relatively prime).