What is the Greatest Common Factor of 15249 and 15264?

Greatest common factor (GCF) of 15249 and 15264 is 3.

GCF(15249,15264) = 3

We will now calculate the prime factors of 15249 and 15264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15249 and 15264.

How to find the GCF of 15249 and 15264?

We will first find the prime factorization of 15249 and 15264. After we will calculate the factors of 15249 and 15264 and find the biggest common factor number .

Step-1: Prime Factorization of 15249

Prime factors of 15249 are 3, 13, 17, 23. Prime factorization of 15249 in exponential form is:

15249 = 3¹ × 13¹ × 17¹ × 23¹

Step-2: Prime Factorization of 15264

Prime factors of 15264 are 2, 3, 53. Prime factorization of 15264 in exponential form is:

15264 = 2⁵ × 3² × 53¹

Step-3: Factors of 15249

List of positive integer factors of 15249 that divides 15249 without a remainder.

1, 3, 13, 17, 23, 39, 51, 69, 221, 299, 391, 663, 897, 1173, 5083

Step-4: Factors of 15264

List of positive integer factors of 15264 that divides 15249 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 53, 72, 96, 106, 144, 159, 212, 288, 318, 424, 477, 636, 848, 954, 1272, 1696, 1908, 2544, 3816, 5088, 7632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15249 and 15264. The biggest common factor number is the GCF number.
So the greatest common factor 15249 and 15264 is 3.

Also check out the Least Common Multiple of 15249 and 15264