Method 1:

List the factors of each number.

Factors of 54 : 2, 3, 6, 9, 18, 27, 54

Factors of 89 : 89

Identify the greatest common factor.

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

So, the greatest common factor is 1

Method 2:

Write the prime factorization of each  number.

54 = 2 × 3 × 3 × 3.

89 = 89.

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

So, the greatest common factor is 1

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