What is the Greatest Common Factor of 960 and 972?

Greatest common factor (GCF) of 960 and 972 is 12.

GCF(960,972) = 12

We will now calculate the prime factors of 960 and 972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 960 and 972.

How to find the GCF of 960 and 972?

We will first find the prime factorization of 960 and 972. After we will calculate the factors of 960 and 972 and find the biggest common factor number .

Step-1: Prime Factorization of 960

Prime factors of 960 are 2, 3, 5. Prime factorization of 960 in exponential form is:

960 = 2⁶ × 3¹ × 5¹

Step-2: Prime Factorization of 972

Prime factors of 972 are 2, 3. Prime factorization of 972 in exponential form is:

972 = 2² × 3⁵

Step-3: Factors of 960

List of positive integer factors of 960 that divides 960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480

Step-4: Factors of 972

List of positive integer factors of 972 that divides 960 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 960 and 972. The biggest common factor number is the GCF number.
So the greatest common factor 960 and 972 is 12.

Also check out the Least Common Multiple of 960 and 972