What is the Greatest Common Factor of 960 and 975?

Greatest common factor (GCF) of 960 and 975 is 15.

GCF(960,975) = 15

We will now calculate the prime factors of 960 and 975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 960 and 975.

How to find the GCF of 960 and 975?

We will first find the prime factorization of 960 and 975. After we will calculate the factors of 960 and 975 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 975

Prime factors of 975 are 3, 5, 13. Prime factorization of 975 in exponential form is:

975 = 3¹ × 5² × 13¹

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 975

List of positive integer factors of 975 that divides 960 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 960 and 975. The biggest common factor number is the GCF number.
So the greatest common factor 960 and 975 is 15.

Also check out the Least Common Multiple of 960 and 975