What is the Greatest Common Factor of 14625 and 14643?

Greatest common factor (GCF) of 14625 and 14643 is 9.

GCF(14625,14643) = 9

We will now calculate the prime factors of 14625 and 14643, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14625 and 14643.

How to find the GCF of 14625 and 14643?

We will first find the prime factorization of 14625 and 14643. After we will calculate the factors of 14625 and 14643 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 14643

Prime factors of 14643 are 3, 1627. Prime factorization of 14643 in exponential form is:

14643 = 3² × 1627¹

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 14643

List of positive integer factors of 14643 that divides 14625 without a remainder.

1, 3, 9, 1627, 4881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14625 and 14643. The biggest common factor number is the GCF number.
So the greatest common factor 14625 and 14643 is 9.

Also check out the Least Common Multiple of 14625 and 14643