What is the Greatest Common Factor of 54285 and 54300?

Greatest common factor (GCF) of 54285 and 54300 is 15.

GCF(54285,54300) = 15

We will now calculate the prime factors of 54285 and 54300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54285 and 54300.

How to find the GCF of 54285 and 54300?

We will first find the prime factorization of 54285 and 54300. After we will calculate the factors of 54285 and 54300 and find the biggest common factor number .

Step-1: Prime Factorization of 54285

Prime factors of 54285 are 3, 5, 7, 11, 47. Prime factorization of 54285 in exponential form is:

54285 = 3¹ × 5¹ × 7¹ × 11¹ × 47¹

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 54285

List of positive integer factors of 54285 that divides 54285 without a remainder.

1, 3, 5, 7, 11, 15, 21, 33, 35, 47, 55, 77, 105, 141, 165, 231, 235, 329, 385, 517, 705, 987, 1155, 1551, 1645, 2585, 3619, 4935, 7755, 10857, 18095

Step-4: Factors of 54300

List of positive integer factors of 54300 that divides 54285 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 54285 and 54300. The biggest common factor number is the GCF number.
So the greatest common factor 54285 and 54300 is 15.

Also check out the Least Common Multiple of 54285 and 54300