What is the Greatest Common Factor of 972 and 984?

Greatest common factor (GCF) of 972 and 984 is 12.

GCF(972,984) = 12

We will now calculate the prime factors of 972 and 984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 972 and 984.

How to find the GCF of 972 and 984?

We will first find the prime factorization of 972 and 984. After we will calculate the factors of 972 and 984 and find the biggest common factor number .

Step-1: Prime Factorization of 972

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

972 = 2² × 3⁵

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 972

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

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

Step-4: Factors of 984

List of positive integer factors of 984 that divides 972 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 972 and 984. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 984 is 12.

Also check out the Least Common Multiple of 972 and 984