Method 1:

List the factors of each number.

Factors of 9 : 3, 9

Factors of 26 : 2 , 13, 26

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.

9 =  3 × 3.

26 =  2 × 13.

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.