What is the gcf of 36 and 54? How to find the greatest common factor of 36 and 54?

Problem. Find the greatest common factor of 36 and 54.

Solution.

See How to find the greatest common factor of two numbers?

The prime factorization of 36

36 =

2 * 2 * 3 * 3

2 * 2 * 3 * 3

The prime factorization of 54

54 =

2 * 3 * 3 * 3

2 * 3 * 3 * 3

Find the common prime factors of these two numbers 36 and 54

36 –> (2, 2, 3, 3)

54 –> (2, 3, 3, 3)

54 –> (2, 3, 3, 3)

The common factors of 36 and 54 are

2, 3, 3

The product of these common prime factors is the greatest common factor of 36 and 54

2 * 3 * 3 = 18

The gcf of 36 and 54 is 18

gcf(36, 54) = 18

The problem is solved.