What is the Greatest Common Factor of 6975 and 6984?

Greatest common factor (GCF) of 6975 and 6984 is 9.

GCF(6975,6984) = 9

We will now calculate the prime factors of 6975 and 6984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6975 and 6984.

How to find the GCF of 6975 and 6984?

We will first find the prime factorization of 6975 and 6984. After we will calculate the factors of 6975 and 6984 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 6984

Prime factors of 6984 are 2, 3, 97. Prime factorization of 6984 in exponential form is:

6984 = 2³ × 3² × 97¹

Step-3: Factors of 6975

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

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

Step-4: Factors of 6984

List of positive integer factors of 6984 that divides 6975 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 97, 194, 291, 388, 582, 776, 873, 1164, 1746, 2328, 3492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6975 and 6984. The biggest common factor number is the GCF number.
So the greatest common factor 6975 and 6984 is 9.

Also check out the Least Common Multiple of 6975 and 6984