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.Three 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 =  2 × 7 .

8 =  2 × 2 × 2 . \ \

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

so, the GCF is  1.

Yes,those numbers are relatively prime.

Yes.