What is the Greatest Common Factor of 54549 and 54564?

Greatest common factor (GCF) of 54549 and 54564 is 3.

GCF(54549,54564) = 3

We will now calculate the prime factors of 54549 and 54564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54549 and 54564.

How to find the GCF of 54549 and 54564?

We will first find the prime factorization of 54549 and 54564. After we will calculate the factors of 54549 and 54564 and find the biggest common factor number .

Step-1: Prime Factorization of 54549

Prime factors of 54549 are 3, 11, 19, 29. Prime factorization of 54549 in exponential form is:

54549 = 3² × 11¹ × 19¹ × 29¹

Step-2: Prime Factorization of 54564

Prime factors of 54564 are 2, 3, 4547. Prime factorization of 54564 in exponential form is:

54564 = 2² × 3¹ × 4547¹

Step-3: Factors of 54549

List of positive integer factors of 54549 that divides 54549 without a remainder.

1, 3, 9, 11, 19, 29, 33, 57, 87, 99, 171, 209, 261, 319, 551, 627, 957, 1653, 1881, 2871, 4959, 6061, 18183

Step-4: Factors of 54564

List of positive integer factors of 54564 that divides 54549 without a remainder.

1, 2, 3, 4, 6, 12, 4547, 9094, 13641, 18188, 27282

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54549 and 54564. The biggest common factor number is the GCF number.
So the greatest common factor 54549 and 54564 is 3.

Also check out the Least Common Multiple of 54549 and 54564