What is the Greatest Common Factor of 972 and 980?

Greatest common factor (GCF) of 972 and 980 is 4.

GCF(972,980) = 4

We will now calculate the prime factors of 972 and 980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 972 and 980.

How to find the GCF of 972 and 980?

We will first find the prime factorization of 972 and 980. After we will calculate the factors of 972 and 980 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 980

Prime factors of 980 are 2, 5, 7. Prime factorization of 980 in exponential form is:

980 = 2² × 5¹ × 7²

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 980

List of positive integer factors of 980 that divides 972 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 972 and 980. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 980 is 4.

Also check out the Least Common Multiple of 972 and 980