What is the Greatest Common Factor of 972 and 987?

Greatest common factor (GCF) of 972 and 987 is 3.

GCF(972,987) = 3

We will now calculate the prime factors of 972 and 987, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 972 and 987.

How to find the GCF of 972 and 987?

We will first find the prime factorization of 972 and 987. After we will calculate the factors of 972 and 987 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 987

Prime factors of 987 are 3, 7, 47. Prime factorization of 987 in exponential form is:

987 = 3¹ × 7¹ × 47¹

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 987

List of positive integer factors of 987 that divides 972 without a remainder.

1, 3, 7, 21, 47, 141, 329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 972 and 987. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 987 is 3.

Also check out the Least Common Multiple of 972 and 987