What is the Greatest Common Factor of 54275 and 54288?

Greatest common factor (GCF) of 54275 and 54288 is 13.

GCF(54275,54288) = 13

We will now calculate the prime factors of 54275 and 54288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54275 and 54288.

How to find the GCF of 54275 and 54288?

We will first find the prime factorization of 54275 and 54288. After we will calculate the factors of 54275 and 54288 and find the biggest common factor number .

Step-1: Prime Factorization of 54275

Prime factors of 54275 are 5, 13, 167. Prime factorization of 54275 in exponential form is:

54275 = 5² × 13¹ × 167¹

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 54275

List of positive integer factors of 54275 that divides 54275 without a remainder.

1, 5, 13, 25, 65, 167, 325, 835, 2171, 4175, 10855

Step-4: Factors of 54288

List of positive integer factors of 54288 that divides 54275 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 54275 and 54288. The biggest common factor number is the GCF number.
So the greatest common factor 54275 and 54288 is 13.

Also check out the Least Common Multiple of 54275 and 54288