What is the Greatest Common Factor of 15342 and 15360?

Greatest common factor (GCF) of 15342 and 15360 is 6.

GCF(15342,15360) = 6

We will now calculate the prime factors of 15342 and 15360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15342 and 15360.

How to find the GCF of 15342 and 15360?

We will first find the prime factorization of 15342 and 15360. After we will calculate the factors of 15342 and 15360 and find the biggest common factor number .

Step-1: Prime Factorization of 15342

Prime factors of 15342 are 2, 3, 2557. Prime factorization of 15342 in exponential form is:

15342 = 2¹ × 3¹ × 2557¹

Step-2: 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-3: Factors of 15342

List of positive integer factors of 15342 that divides 15342 without a remainder.

1, 2, 3, 6, 2557, 5114, 7671

Step-4: Factors of 15360

List of positive integer factors of 15360 that divides 15342 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15342 and 15360. The biggest common factor number is the GCF number.
So the greatest common factor 15342 and 15360 is 6.

Also check out the Least Common Multiple of 15342 and 15360