What is the Greatest Common Factor of 972 and 990?

Greatest common factor (GCF) of 972 and 990 is 18.

GCF(972,990) = 18

We will now calculate the prime factors of 972 and 990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 972 and 990.

How to find the GCF of 972 and 990?

We will first find the prime factorization of 972 and 990. After we will calculate the factors of 972 and 990 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 990

Prime factors of 990 are 2, 3, 5, 11. Prime factorization of 990 in exponential form is:

990 = 2¹ × 3² × 5¹ × 11¹

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 990

List of positive integer factors of 990 that divides 972 without a remainder.

1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 972 and 990. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 990 is 18.

Also check out the Least Common Multiple of 972 and 990