Method 1:

List the factors of each number.

Factors of 13: 1 , 13.

Factors of 11: 1 , 11.

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.

13 =  1 × 13.

11 =  1 × 11.

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.