What is the Greatest Common Factor of 54978 and 54992?

Greatest common factor (GCF) of 54978 and 54992 is 14.

GCF(54978,54992) = 14

We will now calculate the prime factors of 54978 and 54992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54978 and 54992.

How to find the GCF of 54978 and 54992?

We will first find the prime factorization of 54978 and 54992. After we will calculate the factors of 54978 and 54992 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54992

Prime factors of 54992 are 2, 7, 491. Prime factorization of 54992 in exponential form is:

54992 = 2⁴ × 7¹ × 491¹

Step-3: Factors of 54978

List of positive integer factors of 54978 that divides 54978 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

Step-4: Factors of 54992

List of positive integer factors of 54992 that divides 54978 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 491, 982, 1964, 3437, 3928, 6874, 7856, 13748, 27496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54978 and 54992. The biggest common factor number is the GCF number.
So the greatest common factor 54978 and 54992 is 14.

Also check out the Least Common Multiple of 54978 and 54992