What is the Greatest Common Factor of 54964 and 54978?

Greatest common factor (GCF) of 54964 and 54978 is 14.

GCF(54964,54978) = 14

We will now calculate the prime factors of 54964 and 54978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54964 and 54978.

How to find the GCF of 54964 and 54978?

We will first find the prime factorization of 54964 and 54978. After we will calculate the factors of 54964 and 54978 and find the biggest common factor number .

Step-1: Prime Factorization of 54964

Prime factors of 54964 are 2, 7, 13, 151. Prime factorization of 54964 in exponential form is:

54964 = 2² × 7¹ × 13¹ × 151¹

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 54964

List of positive integer factors of 54964 that divides 54964 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 151, 182, 302, 364, 604, 1057, 1963, 2114, 3926, 4228, 7852, 13741, 27482

Step-4: Factors of 54978

List of positive integer factors of 54978 that divides 54964 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 54964 and 54978. The biggest common factor number is the GCF number.
So the greatest common factor 54964 and 54978 is 14.

Also check out the Least Common Multiple of 54964 and 54978