What is the Greatest Common Factor of 54960 and 54972?

Greatest common factor (GCF) of 54960 and 54972 is 12.

GCF(54960,54972) = 12

We will now calculate the prime factors of 54960 and 54972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54960 and 54972.

How to find the GCF of 54960 and 54972?

We will first find the prime factorization of 54960 and 54972. After we will calculate the factors of 54960 and 54972 and find the biggest common factor number .

Step-1: Prime Factorization of 54960

Prime factors of 54960 are 2, 3, 5, 229. Prime factorization of 54960 in exponential form is:

54960 = 2⁴ × 3¹ × 5¹ × 229¹

Step-2: Prime Factorization of 54972

Prime factors of 54972 are 2, 3, 509. Prime factorization of 54972 in exponential form is:

54972 = 2² × 3³ × 509¹

Step-3: Factors of 54960

List of positive integer factors of 54960 that divides 54960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 229, 240, 458, 687, 916, 1145, 1374, 1832, 2290, 2748, 3435, 3664, 4580, 5496, 6870, 9160, 10992, 13740, 18320, 27480

Step-4: Factors of 54972

List of positive integer factors of 54972 that divides 54960 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 509, 1018, 1527, 2036, 3054, 4581, 6108, 9162, 13743, 18324, 27486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54960 and 54972. The biggest common factor number is the GCF number.
So the greatest common factor 54960 and 54972 is 12.

Also check out the Least Common Multiple of 54960 and 54972