What is the Greatest Common Factor of 972 and 992?

Greatest common factor (GCF) of 972 and 992 is 4.

GCF(972,992) = 4

We will now calculate the prime factors of 972 and 992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 972 and 992.

How to find the GCF of 972 and 992?

We will first find the prime factorization of 972 and 992. After we will calculate the factors of 972 and 992 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 992

Prime factors of 992 are 2, 31. Prime factorization of 992 in exponential form is:

992 = 2⁵ × 31¹

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 992

List of positive integer factors of 992 that divides 972 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 972 and 992. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 992 is 4.

Also check out the Least Common Multiple of 972 and 992