What is the Greatest Common Factor of 25627 and 25634?

Greatest common factor (GCF) of 25627 and 25634 is 7.

GCF(25627,25634) = 7

We will now calculate the prime factors of 25627 and 25634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25627 and 25634.

How to find the GCF of 25627 and 25634?

We will first find the prime factorization of 25627 and 25634. After we will calculate the factors of 25627 and 25634 and find the biggest common factor number .

Step-1: Prime Factorization of 25627

Prime factors of 25627 are 7, 523. Prime factorization of 25627 in exponential form is:

25627 = 7² × 523¹

Step-2: Prime Factorization of 25634

Prime factors of 25634 are 2, 7, 1831. Prime factorization of 25634 in exponential form is:

25634 = 2¹ × 7¹ × 1831¹

Step-3: Factors of 25627

List of positive integer factors of 25627 that divides 25627 without a remainder.

1, 7, 49, 523, 3661

Step-4: Factors of 25634

List of positive integer factors of 25634 that divides 25627 without a remainder.

1, 2, 7, 14, 1831, 3662, 12817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25627 and 25634. The biggest common factor number is the GCF number.
So the greatest common factor 25627 and 25634 is 7.

Also check out the Least Common Multiple of 25627 and 25634