What is the Greatest Common Factor of 15360 and 15375?

Greatest common factor (GCF) of 15360 and 15375 is 15.

GCF(15360,15375) = 15

We will now calculate the prime factors of 15360 and 15375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15360 and 15375.

How to find the GCF of 15360 and 15375?

We will first find the prime factorization of 15360 and 15375. After we will calculate the factors of 15360 and 15375 and find the biggest common factor number .

Step-1: Prime Factorization of 15360

Prime factors of 15360 are 2, 3, 5. Prime factorization of 15360 in exponential form is:

15360 = 2¹⁰ × 3¹ × 5¹

Step-2: Prime Factorization of 15375

Prime factors of 15375 are 3, 5, 41. Prime factorization of 15375 in exponential form is:

15375 = 3¹ × 5³ × 41¹

Step-3: Factors of 15360

List of positive integer factors of 15360 that divides 15360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2560, 3072, 3840, 5120, 7680

Step-4: Factors of 15375

List of positive integer factors of 15375 that divides 15360 without a remainder.

1, 3, 5, 15, 25, 41, 75, 123, 125, 205, 375, 615, 1025, 3075, 5125

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15360 and 15375. The biggest common factor number is the GCF number.
So the greatest common factor 15360 and 15375 is 15.

Also check out the Least Common Multiple of 15360 and 15375