What is the Greatest Common Factor of 14625 and 14641?

Greatest common factor (GCF) of 14625 and 14641 is 1.

GCF(14625,14641) = 1

We will now calculate the prime factors of 14625 and 14641, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14625 and 14641.

How to find the GCF of 14625 and 14641?

We will first find the prime factorization of 14625 and 14641. After we will calculate the factors of 14625 and 14641 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 14641

Prime factors of 14641 are 11. Prime factorization of 14641 in exponential form is:

14641 = 11⁴

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 14641

List of positive integer factors of 14641 that divides 14625 without a remainder.

1, 11, 121, 1331

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14625 and 14641. The biggest common factor number is the GCF number.
So the greatest common factor 14625 and 14641 is 1.

Also check out the Least Common Multiple of 14625 and 14641