What is the Greatest Common Factor of 12675 and 12688?

Greatest common factor (GCF) of 12675 and 12688 is 13.

GCF(12675,12688) = 13

We will now calculate the prime factors of 12675 and 12688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12675 and 12688.

How to find the GCF of 12675 and 12688?

We will first find the prime factorization of 12675 and 12688. After we will calculate the factors of 12675 and 12688 and find the biggest common factor number .

Step-1: Prime Factorization of 12675

Prime factors of 12675 are 3, 5, 13. Prime factorization of 12675 in exponential form is:

12675 = 3¹ × 5² × 13²

Step-2: Prime Factorization of 12688

Prime factors of 12688 are 2, 13, 61. Prime factorization of 12688 in exponential form is:

12688 = 2⁴ × 13¹ × 61¹

Step-3: Factors of 12675

List of positive integer factors of 12675 that divides 12675 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 75, 169, 195, 325, 507, 845, 975, 2535, 4225

Step-4: Factors of 12688

List of positive integer factors of 12688 that divides 12675 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 61, 104, 122, 208, 244, 488, 793, 976, 1586, 3172, 6344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12675 and 12688. The biggest common factor number is the GCF number.
So the greatest common factor 12675 and 12688 is 13.

Also check out the Least Common Multiple of 12675 and 12688