What is the Greatest Common Factor of 975 and 984?

Greatest common factor (GCF) of 975 and 984 is 3.

GCF(975,984) = 3

We will now calculate the prime factors of 975 and 984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 975 and 984.

How to find the GCF of 975 and 984?

We will first find the prime factorization of 975 and 984. After we will calculate the factors of 975 and 984 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 984

Prime factors of 984 are 2, 3, 41. Prime factorization of 984 in exponential form is:

984 = 2³ × 3¹ × 41¹

Step-3: Factors of 975

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

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

Step-4: Factors of 984

List of positive integer factors of 984 that divides 975 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 975 and 984. The biggest common factor number is the GCF number.
So the greatest common factor 975 and 984 is 3.

Also check out the Least Common Multiple of 975 and 984