What is the Greatest Common Factor of 54272 and 54288?

Greatest common factor (GCF) of 54272 and 54288 is 16.

GCF(54272,54288) = 16

We will now calculate the prime factors of 54272 and 54288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54272 and 54288.

How to find the GCF of 54272 and 54288?

We will first find the prime factorization of 54272 and 54288. After we will calculate the factors of 54272 and 54288 and find the biggest common factor number .

Step-1: Prime Factorization of 54272

Prime factors of 54272 are 2, 53. Prime factorization of 54272 in exponential form is:

54272 = 2¹⁰ × 53¹

Step-2: Prime Factorization of 54288

Prime factors of 54288 are 2, 3, 13, 29. Prime factorization of 54288 in exponential form is:

54288 = 2⁴ × 3² × 13¹ × 29¹

Step-3: Factors of 54272

List of positive integer factors of 54272 that divides 54272 without a remainder.

1, 2, 4, 8, 16, 32, 53, 64, 106, 128, 212, 256, 424, 512, 848, 1024, 1696, 3392, 6784, 13568, 27136

Step-4: Factors of 54288

List of positive integer factors of 54288 that divides 54272 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 29, 36, 39, 48, 52, 58, 72, 78, 87, 104, 116, 117, 144, 156, 174, 208, 232, 234, 261, 312, 348, 377, 464, 468, 522, 624, 696, 754, 936, 1044, 1131, 1392, 1508, 1872, 2088, 2262, 3016, 3393, 4176, 4524, 6032, 6786, 9048, 13572, 18096, 27144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54272 and 54288. The biggest common factor number is the GCF number.
So the greatest common factor 54272 and 54288 is 16.

Also check out the Least Common Multiple of 54272 and 54288