What is the Greatest Common Factor of 12564 and 12584?

Greatest common factor (GCF) of 12564 and 12584 is 4.

GCF(12564,12584) = 4

We will now calculate the prime factors of 12564 and 12584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12564 and 12584.

How to find the GCF of 12564 and 12584?

We will first find the prime factorization of 12564 and 12584. After we will calculate the factors of 12564 and 12584 and find the biggest common factor number .

Step-1: Prime Factorization of 12564

Prime factors of 12564 are 2, 3, 349. Prime factorization of 12564 in exponential form is:

12564 = 2² × 3² × 349¹

Step-2: Prime Factorization of 12584

Prime factors of 12584 are 2, 11, 13. Prime factorization of 12584 in exponential form is:

12584 = 2³ × 11² × 13¹

Step-3: Factors of 12564

List of positive integer factors of 12564 that divides 12564 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 349, 698, 1047, 1396, 2094, 3141, 4188, 6282

Step-4: Factors of 12584

List of positive integer factors of 12584 that divides 12564 without a remainder.

1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 121, 143, 242, 286, 484, 572, 968, 1144, 1573, 3146, 6292

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12564 and 12584. The biggest common factor number is the GCF number.
So the greatest common factor 12564 and 12584 is 4.

Also check out the Least Common Multiple of 12564 and 12584