What is the Greatest Common Factor of 54609 and 54624?

Greatest common factor (GCF) of 54609 and 54624 is 3.

GCF(54609,54624) = 3

We will now calculate the prime factors of 54609 and 54624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54609 and 54624.

How to find the GCF of 54609 and 54624?

We will first find the prime factorization of 54609 and 54624. After we will calculate the factors of 54609 and 54624 and find the biggest common factor number .

Step-1: Prime Factorization of 54609

Prime factors of 54609 are 3, 109, 167. Prime factorization of 54609 in exponential form is:

54609 = 3¹ × 109¹ × 167¹

Step-2: Prime Factorization of 54624

Prime factors of 54624 are 2, 3, 569. Prime factorization of 54624 in exponential form is:

54624 = 2⁵ × 3¹ × 569¹

Step-3: Factors of 54609

List of positive integer factors of 54609 that divides 54609 without a remainder.

1, 3, 109, 167, 327, 501, 18203

Step-4: Factors of 54624

List of positive integer factors of 54624 that divides 54609 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 569, 1138, 1707, 2276, 3414, 4552, 6828, 9104, 13656, 18208, 27312

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54609 and 54624. The biggest common factor number is the GCF number.
So the greatest common factor 54609 and 54624 is 3.

Also check out the Least Common Multiple of 54609 and 54624