What is the Greatest Common Factor of 120 and 132?

Greatest common factor (GCF) of 120 and 132 is 12.

GCF(120,132) = 12

We will now calculate the prime factors of 120 and 132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 120 and 132.

How to find the GCF of 120 and 132?

We will first find the prime factorization of 120 and 132. After we will calculate the factors of 120 and 132 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 132

Prime factors of 132 are 2, 3, 11. Prime factorization of 132 in exponential form is:

132 = 2² × 3¹ × 11¹

Step-3: Factors of 120

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

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

Step-4: Factors of 132

List of positive integer factors of 132 that divides 120 without a remainder.

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 120 and 132. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 132 is 12.

Also check out the Least Common Multiple of 120 and 132