What is the Greatest Common Factor of 12249 and 12264?

Greatest common factor (GCF) of 12249 and 12264 is 3.

GCF(12249,12264) = 3

We will now calculate the prime factors of 12249 and 12264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12249 and 12264.

How to find the GCF of 12249 and 12264?

We will first find the prime factorization of 12249 and 12264. After we will calculate the factors of 12249 and 12264 and find the biggest common factor number .

Step-1: Prime Factorization of 12249

Prime factors of 12249 are 3, 1361. Prime factorization of 12249 in exponential form is:

12249 = 3² × 1361¹

Step-2: Prime Factorization of 12264

Prime factors of 12264 are 2, 3, 7, 73. Prime factorization of 12264 in exponential form is:

12264 = 2³ × 3¹ × 7¹ × 73¹

Step-3: Factors of 12249

List of positive integer factors of 12249 that divides 12249 without a remainder.

1, 3, 9, 1361, 4083

Step-4: Factors of 12264

List of positive integer factors of 12264 that divides 12249 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 73, 84, 146, 168, 219, 292, 438, 511, 584, 876, 1022, 1533, 1752, 2044, 3066, 4088, 6132

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12249 and 12264. The biggest common factor number is the GCF number.
So the greatest common factor 12249 and 12264 is 3.

Also check out the Least Common Multiple of 12249 and 12264