What is the Greatest Common Factor of 12635 and 12649?

Greatest common factor (GCF) of 12635 and 12649 is 7.

GCF(12635,12649) = 7

We will now calculate the prime factors of 12635 and 12649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12635 and 12649.

How to find the GCF of 12635 and 12649?

We will first find the prime factorization of 12635 and 12649. After we will calculate the factors of 12635 and 12649 and find the biggest common factor number .

Step-1: Prime Factorization of 12635

Prime factors of 12635 are 5, 7, 19. Prime factorization of 12635 in exponential form is:

12635 = 5¹ × 7¹ × 19²

Step-2: Prime Factorization of 12649

Prime factors of 12649 are 7, 13, 139. Prime factorization of 12649 in exponential form is:

12649 = 7¹ × 13¹ × 139¹

Step-3: Factors of 12635

List of positive integer factors of 12635 that divides 12635 without a remainder.

1, 5, 7, 19, 35, 95, 133, 361, 665, 1805, 2527

Step-4: Factors of 12649

List of positive integer factors of 12649 that divides 12635 without a remainder.

1, 7, 13, 91, 139, 973, 1807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12635 and 12649. The biggest common factor number is the GCF number.
So the greatest common factor 12635 and 12649 is 7.

Also check out the Least Common Multiple of 12635 and 12649