What is the Greatest Common Factor of 954 and 972?

Greatest common factor (GCF) of 954 and 972 is 18.

GCF(954,972) = 18

We will now calculate the prime factors of 954 and 972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 954 and 972.

How to find the GCF of 954 and 972?

We will first find the prime factorization of 954 and 972. After we will calculate the factors of 954 and 972 and find the biggest common factor number .

Step-1: Prime Factorization of 954

Prime factors of 954 are 2, 3, 53. Prime factorization of 954 in exponential form is:

954 = 2¹ × 3² × 53¹

Step-2: Prime Factorization of 972

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

972 = 2² × 3⁵

Step-3: Factors of 954

List of positive integer factors of 954 that divides 954 without a remainder.

1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477

Step-4: Factors of 972

List of positive integer factors of 972 that divides 954 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 954 and 972. The biggest common factor number is the GCF number.
So the greatest common factor 954 and 972 is 18.

Also check out the Least Common Multiple of 954 and 972