What is the Greatest Common Factor of 6960 and 6975?

Greatest common factor (GCF) of 6960 and 6975 is 15.

GCF(6960,6975) = 15

We will now calculate the prime factors of 6960 and 6975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6960 and 6975.

How to find the GCF of 6960 and 6975?

We will first find the prime factorization of 6960 and 6975. After we will calculate the factors of 6960 and 6975 and find the biggest common factor number .

Step-1: Prime Factorization of 6960

Prime factors of 6960 are 2, 3, 5, 29. Prime factorization of 6960 in exponential form is:

6960 = 2⁴ × 3¹ × 5¹ × 29¹

Step-2: Prime Factorization of 6975

Prime factors of 6975 are 3, 5, 31. Prime factorization of 6975 in exponential form is:

6975 = 3² × 5² × 31¹

Step-3: Factors of 6960

List of positive integer factors of 6960 that divides 6960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 40, 48, 58, 60, 80, 87, 116, 120, 145, 174, 232, 240, 290, 348, 435, 464, 580, 696, 870, 1160, 1392, 1740, 2320, 3480

Step-4: Factors of 6975

List of positive integer factors of 6975 that divides 6960 without a remainder.

1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6960 and 6975. The biggest common factor number is the GCF number.
So the greatest common factor 6960 and 6975 is 15.

Also check out the Least Common Multiple of 6960 and 6975