What is the Greatest Common Factor of 15360 and 15372?

Greatest common factor (GCF) of 15360 and 15372 is 12.

GCF(15360,15372) = 12

We will now calculate the prime factors of 15360 and 15372, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15360 and 15372.

How to find the GCF of 15360 and 15372?

We will first find the prime factorization of 15360 and 15372. After we will calculate the factors of 15360 and 15372 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 15372

Prime factors of 15372 are 2, 3, 7, 61. Prime factorization of 15372 in exponential form is:

15372 = 2² × 3² × 7¹ × 61¹

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 15372

List of positive integer factors of 15372 that divides 15360 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 61, 63, 84, 122, 126, 183, 244, 252, 366, 427, 549, 732, 854, 1098, 1281, 1708, 2196, 2562, 3843, 5124, 7686

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15360 and 15372. The biggest common factor number is the GCF number.
So the greatest common factor 15360 and 15372 is 12.

Also check out the Least Common Multiple of 15360 and 15372