What is the Greatest Common Factor of 12657 and 12672?

Greatest common factor (GCF) of 12657 and 12672 is 3.

GCF(12657,12672) = 3

We will now calculate the prime factors of 12657 and 12672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12657 and 12672.

How to find the GCF of 12657 and 12672?

We will first find the prime factorization of 12657 and 12672. After we will calculate the factors of 12657 and 12672 and find the biggest common factor number .

Step-1: Prime Factorization of 12657

Prime factors of 12657 are 3, 4219. Prime factorization of 12657 in exponential form is:

12657 = 3¹ × 4219¹

Step-2: Prime Factorization of 12672

Prime factors of 12672 are 2, 3, 11. Prime factorization of 12672 in exponential form is:

12672 = 2⁷ × 3² × 11¹

Step-3: Factors of 12657

List of positive integer factors of 12657 that divides 12657 without a remainder.

1, 3, 4219

Step-4: Factors of 12672

List of positive integer factors of 12672 that divides 12657 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 64, 66, 72, 88, 96, 99, 128, 132, 144, 176, 192, 198, 264, 288, 352, 384, 396, 528, 576, 704, 792, 1056, 1152, 1408, 1584, 2112, 3168, 4224, 6336

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12657 and 12672. The biggest common factor number is the GCF number.
So the greatest common factor 12657 and 12672 is 3.

Also check out the Least Common Multiple of 12657 and 12672