What is the Greatest Common Factor of 12642 and 12656?

Greatest common factor (GCF) of 12642 and 12656 is 14.

GCF(12642,12656) = 14

We will now calculate the prime factors of 12642 and 12656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12642 and 12656.

How to find the GCF of 12642 and 12656?

We will first find the prime factorization of 12642 and 12656. After we will calculate the factors of 12642 and 12656 and find the biggest common factor number .

Step-1: Prime Factorization of 12642

Prime factors of 12642 are 2, 3, 7, 43. Prime factorization of 12642 in exponential form is:

12642 = 2¹ × 3¹ × 7² × 43¹

Step-2: Prime Factorization of 12656

Prime factors of 12656 are 2, 7, 113. Prime factorization of 12656 in exponential form is:

12656 = 2⁴ × 7¹ × 113¹

Step-3: Factors of 12642

List of positive integer factors of 12642 that divides 12642 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 43, 49, 86, 98, 129, 147, 258, 294, 301, 602, 903, 1806, 2107, 4214, 6321

Step-4: Factors of 12656

List of positive integer factors of 12656 that divides 12642 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 113, 226, 452, 791, 904, 1582, 1808, 3164, 6328

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12642 and 12656. The biggest common factor number is the GCF number.
So the greatest common factor 12642 and 12656 is 14.

Also check out the Least Common Multiple of 12642 and 12656