What is the Greatest Common Factor of 14625 and 14640?

Greatest common factor (GCF) of 14625 and 14640 is 15.

GCF(14625,14640) = 15

We will now calculate the prime factors of 14625 and 14640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14625 and 14640.

How to find the GCF of 14625 and 14640?

We will first find the prime factorization of 14625 and 14640. After we will calculate the factors of 14625 and 14640 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 14640

Prime factors of 14640 are 2, 3, 5, 61. Prime factorization of 14640 in exponential form is:

14640 = 2⁴ × 3¹ × 5¹ × 61¹

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 14640

List of positive integer factors of 14640 that divides 14625 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 61, 80, 120, 122, 183, 240, 244, 305, 366, 488, 610, 732, 915, 976, 1220, 1464, 1830, 2440, 2928, 3660, 4880, 7320

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14625 and 14640. The biggest common factor number is the GCF number.
So the greatest common factor 14625 and 14640 is 15.

Also check out the Least Common Multiple of 14625 and 14640