What is the Greatest Common Factor of 120 and 135?

Greatest common factor (GCF) of 120 and 135 is 15.

GCF(120,135) = 15

We will now calculate the prime factors of 120 and 135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 120 and 135.

How to find the GCF of 120 and 135?

We will first find the prime factorization of 120 and 135. After we will calculate the factors of 120 and 135 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 135

Prime factors of 135 are 3, 5. Prime factorization of 135 in exponential form is:

135 = 3³ × 5¹

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 135

List of positive integer factors of 135 that divides 120 without a remainder.

1, 3, 5, 9, 15, 27, 45

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 120 and 135. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 135 is 15.

Also check out the Least Common Multiple of 120 and 135