What is the Greatest Common Factor of 12614 and 12628?

Greatest common factor (GCF) of 12614 and 12628 is 14.

GCF(12614,12628) = 14

We will now calculate the prime factors of 12614 and 12628, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12614 and 12628.

How to find the GCF of 12614 and 12628?

We will first find the prime factorization of 12614 and 12628. After we will calculate the factors of 12614 and 12628 and find the biggest common factor number .

Step-1: Prime Factorization of 12614

Prime factors of 12614 are 2, 7, 17, 53. Prime factorization of 12614 in exponential form is:

12614 = 2¹ × 7¹ × 17¹ × 53¹

Step-2: Prime Factorization of 12628

Prime factors of 12628 are 2, 7, 11, 41. Prime factorization of 12628 in exponential form is:

12628 = 2² × 7¹ × 11¹ × 41¹

Step-3: Factors of 12614

List of positive integer factors of 12614 that divides 12614 without a remainder.

1, 2, 7, 14, 17, 34, 53, 106, 119, 238, 371, 742, 901, 1802, 6307

Step-4: Factors of 12628

List of positive integer factors of 12628 that divides 12614 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 41, 44, 77, 82, 154, 164, 287, 308, 451, 574, 902, 1148, 1804, 3157, 6314

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12614 and 12628. The biggest common factor number is the GCF number.
So the greatest common factor 12614 and 12628 is 14.

Also check out the Least Common Multiple of 12614 and 12628