Method 1:

List the factors of each number.

Factors of 77 : 7, 11, 77

Factors of 51: 3, 17, 51

Identify the greatest common factor.

There are  no common prime factors.Two numbers always have 1 as a common factor.

So, the GCF is 1, and the numbers are relatively prime.

Method 2:

Write the prime factorization of each  number.

77  =  7 × 11.

51 =  3 × 17.

There are  no common prime factors.Two numbers always have 1 as a common factor.

So, the GCF is 1, and the numbers are relatively prime.

There are  no common prime factors.Two numbers always have 1 as a common factor.So, the GCF is 1, and the numbers are relatively prime.