What is the Greatest Common Factor of 54300 and 54312?

Greatest common factor (GCF) of 54300 and 54312 is 12.

GCF(54300,54312) = 12

We will now calculate the prime factors of 54300 and 54312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54300 and 54312.

How to find the GCF of 54300 and 54312?

We will first find the prime factorization of 54300 and 54312. After we will calculate the factors of 54300 and 54312 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54312

Prime factors of 54312 are 2, 3, 31, 73. Prime factorization of 54312 in exponential form is:

54312 = 2³ × 3¹ × 31¹ × 73¹

Step-3: Factors of 54300

List of positive integer factors of 54300 that divides 54300 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

Step-4: Factors of 54312

List of positive integer factors of 54312 that divides 54300 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 73, 93, 124, 146, 186, 219, 248, 292, 372, 438, 584, 744, 876, 1752, 2263, 4526, 6789, 9052, 13578, 18104, 27156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54300 and 54312. The biggest common factor number is the GCF number.
So the greatest common factor 54300 and 54312 is 12.

Also check out the Least Common Multiple of 54300 and 54312