What is the Greatest Common Factor of 8625 and 8640?

Greatest common factor (GCF) of 8625 and 8640 is 15.

GCF(8625,8640) = 15

We will now calculate the prime factors of 8625 and 8640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8625 and 8640.

How to find the GCF of 8625 and 8640?

We will first find the prime factorization of 8625 and 8640. After we will calculate the factors of 8625 and 8640 and find the biggest common factor number .

Step-1: Prime Factorization of 8625

Prime factors of 8625 are 3, 5, 23. Prime factorization of 8625 in exponential form is:

8625 = 3¹ × 5³ × 23¹

Step-2: Prime Factorization of 8640

Prime factors of 8640 are 2, 3, 5. Prime factorization of 8640 in exponential form is:

8640 = 2⁶ × 3³ × 5¹

Step-3: Factors of 8625

List of positive integer factors of 8625 that divides 8625 without a remainder.

1, 3, 5, 15, 23, 25, 69, 75, 115, 125, 345, 375, 575, 1725, 2875

Step-4: Factors of 8640

List of positive integer factors of 8640 that divides 8625 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 192, 216, 240, 270, 288, 320, 360, 432, 480, 540, 576, 720, 864, 960, 1080, 1440, 1728, 2160, 2880, 4320

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8625 and 8640. The biggest common factor number is the GCF number.
So the greatest common factor 8625 and 8640 is 15.

Also check out the Least Common Multiple of 8625 and 8640