What is the Greatest Common Factor of 54264 and 54278?

Greatest common factor (GCF) of 54264 and 54278 is 14.

GCF(54264,54278) = 14

We will now calculate the prime factors of 54264 and 54278, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54264 and 54278.

How to find the GCF of 54264 and 54278?

We will first find the prime factorization of 54264 and 54278. After we will calculate the factors of 54264 and 54278 and find the biggest common factor number .

Step-1: Prime Factorization of 54264

Prime factors of 54264 are 2, 3, 7, 17, 19. Prime factorization of 54264 in exponential form is:

54264 = 2³ × 3¹ × 7¹ × 17¹ × 19¹

Step-2: Prime Factorization of 54278

Prime factors of 54278 are 2, 7, 3877. Prime factorization of 54278 in exponential form is:

54278 = 2¹ × 7¹ × 3877¹

Step-3: Factors of 54264

List of positive integer factors of 54264 that divides 54264 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 19, 21, 24, 28, 34, 38, 42, 51, 56, 57, 68, 76, 84, 102, 114, 119, 133, 136, 152, 168, 204, 228, 238, 266, 323, 357, 399, 408, 456, 476, 532, 646, 714, 798, 952, 969, 1064, 1292, 1428, 1596, 1938, 2261, 2584, 2856, 3192, 3876, 4522, 6783, 7752, 9044, 13566, 18088, 27132

Step-4: Factors of 54278

List of positive integer factors of 54278 that divides 54264 without a remainder.

1, 2, 7, 14, 3877, 7754, 27139

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54264 and 54278. The biggest common factor number is the GCF number.
So the greatest common factor 54264 and 54278 is 14.

Also check out the Least Common Multiple of 54264 and 54278