What is the Greatest Common Factor of 54288 and 54300?

Greatest common factor (GCF) of 54288 and 54300 is 12.

GCF(54288,54300) = 12

We will now calculate the prime factors of 54288 and 54300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54288 and 54300.

How to find the GCF of 54288 and 54300?

We will first find the prime factorization of 54288 and 54300. After we will calculate the factors of 54288 and 54300 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54300

Prime factors of 54300 are 2, 3, 5, 181. Prime factorization of 54300 in exponential form is:

54300 = 2² × 3¹ × 5² × 181¹

Step-3: Factors of 54288

List of positive integer factors of 54288 that divides 54288 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

Step-4: Factors of 54300

List of positive integer factors of 54300 that divides 54288 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 181, 300, 362, 543, 724, 905, 1086, 1810, 2172, 2715, 3620, 4525, 5430, 9050, 10860, 13575, 18100, 27150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54288 and 54300. The biggest common factor number is the GCF number.
So the greatest common factor 54288 and 54300 is 12.

Also check out the Least Common Multiple of 54288 and 54300