What is the Greatest Common Factor of 108 and 120?

Greatest common factor (GCF) of 108 and 120 is 12.

GCF(108,120) = 12

We will now calculate the prime factors of 108 and 120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 108 and 120.

How to find the GCF of 108 and 120?

We will first find the prime factorization of 108 and 120. After we will calculate the factors of 108 and 120 and find the biggest common factor number .

Step-1: Prime Factorization of 108

Prime factors of 108 are 2, 3. Prime factorization of 108 in exponential form is:

108 = 2² × 3³

Step-2: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 2³ × 3¹ × 5¹

Step-3: Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54

Step-4: Factors of 120

List of positive integer factors of 120 that divides 108 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 108 and 120. The biggest common factor number is the GCF number.
So the greatest common factor 108 and 120 is 12.

Also check out the Least Common Multiple of 108 and 120