What is the Greatest Common Factor of 14625 and 14634?

Greatest common factor (GCF) of 14625 and 14634 is 9.

GCF(14625,14634) = 9

We will now calculate the prime factors of 14625 and 14634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14625 and 14634.

How to find the GCF of 14625 and 14634?

We will first find the prime factorization of 14625 and 14634. After we will calculate the factors of 14625 and 14634 and find the biggest common factor number .

Step-1: Prime Factorization of 14625

Prime factors of 14625 are 3, 5, 13. Prime factorization of 14625 in exponential form is:

14625 = 3² × 5³ × 13¹

Step-2: Prime Factorization of 14634

Prime factors of 14634 are 2, 3, 271. Prime factorization of 14634 in exponential form is:

14634 = 2¹ × 3³ × 271¹

Step-3: Factors of 14625

List of positive integer factors of 14625 that divides 14625 without a remainder.

1, 3, 5, 9, 13, 15, 25, 39, 45, 65, 75, 117, 125, 195, 225, 325, 375, 585, 975, 1125, 1625, 2925, 4875

Step-4: Factors of 14634

List of positive integer factors of 14634 that divides 14625 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 271, 542, 813, 1626, 2439, 4878, 7317

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14625 and 14634. The biggest common factor number is the GCF number.
So the greatest common factor 14625 and 14634 is 9.

Also check out the Least Common Multiple of 14625 and 14634