What is the Greatest Common Factor of 15360 and 15365?

Greatest common factor (GCF) of 15360 and 15365 is 5.

GCF(15360,15365) = 5

We will now calculate the prime factors of 15360 and 15365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15360 and 15365.

How to find the GCF of 15360 and 15365?

We will first find the prime factorization of 15360 and 15365. After we will calculate the factors of 15360 and 15365 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 15365

Prime factors of 15365 are 5, 7, 439. Prime factorization of 15365 in exponential form is:

15365 = 5¹ × 7¹ × 439¹

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 15365

List of positive integer factors of 15365 that divides 15360 without a remainder.

1, 5, 7, 35, 439, 2195, 3073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15360 and 15365. The biggest common factor number is the GCF number.
So the greatest common factor 15360 and 15365 is 5.

Also check out the Least Common Multiple of 15360 and 15365