Method 1:

List the factors of each number.

Factors of 7: 1 , 7.

Factors of 8: 1 , 2 , 4 , 8.

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

so, the GCF is  1.

Yes,those numbers are relatively prime.

Method 2:

Write the prime factorization of each  number.

7 =  1 × 7.

8 =  2 × 2 × 2.

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

so, the GCF is  1.

Yes,those numbers are relatively prime.

Yes.