What is the Greatest Common Factor of 54960 and 54978?

Greatest common factor (GCF) of 54960 and 54978 is 6.

GCF(54960,54978) = 6

We will now calculate the prime factors of 54960 and 54978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54960 and 54978.

How to find the GCF of 54960 and 54978?

We will first find the prime factorization of 54960 and 54978. After we will calculate the factors of 54960 and 54978 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 54978

Prime factors of 54978 are 2, 3, 7, 11, 17. Prime factorization of 54978 in exponential form is:

54978 = 2¹ × 3¹ × 7² × 11¹ × 17¹

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 54978

List of positive integer factors of 54978 that divides 54960 without a remainder.

1, 2, 3, 6, 7, 11, 14, 17, 21, 22, 33, 34, 42, 49, 51, 66, 77, 98, 102, 119, 147, 154, 187, 231, 238, 294, 357, 374, 462, 539, 561, 714, 833, 1078, 1122, 1309, 1617, 1666, 2499, 2618, 3234, 3927, 4998, 7854, 9163, 18326, 27489

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54960 and 54978. The biggest common factor number is the GCF number.
So the greatest common factor 54960 and 54978 is 6.

Also check out the Least Common Multiple of 54960 and 54978