What is the Greatest Common Factor of 54249 and 54264?

Greatest common factor (GCF) of 54249 and 54264 is 3.

GCF(54249,54264) = 3

We will now calculate the prime factors of 54249 and 54264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54249 and 54264.

How to find the GCF of 54249 and 54264?

We will first find the prime factorization of 54249 and 54264. After we will calculate the factors of 54249 and 54264 and find the biggest common factor number .

Step-1: Prime Factorization of 54249

Prime factors of 54249 are 3, 13, 107. Prime factorization of 54249 in exponential form is:

54249 = 3¹ × 13² × 107¹

Step-2: 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-3: Factors of 54249

List of positive integer factors of 54249 that divides 54249 without a remainder.

1, 3, 13, 39, 107, 169, 321, 507, 1391, 4173, 18083

Step-4: Factors of 54264

List of positive integer factors of 54264 that divides 54249 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54249 and 54264. The biggest common factor number is the GCF number.
So the greatest common factor 54249 and 54264 is 3.

Also check out the Least Common Multiple of 54249 and 54264