What is the Greatest Common Factor of 12189 and 12204?

Greatest common factor (GCF) of 12189 and 12204 is 3.

GCF(12189,12204) = 3

We will now calculate the prime factors of 12189 and 12204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12189 and 12204.

How to find the GCF of 12189 and 12204?

We will first find the prime factorization of 12189 and 12204. After we will calculate the factors of 12189 and 12204 and find the biggest common factor number .

Step-1: Prime Factorization of 12189

Prime factors of 12189 are 3, 17, 239. Prime factorization of 12189 in exponential form is:

12189 = 3¹ × 17¹ × 239¹

Step-2: Prime Factorization of 12204

Prime factors of 12204 are 2, 3, 113. Prime factorization of 12204 in exponential form is:

12204 = 2² × 3³ × 113¹

Step-3: Factors of 12189

List of positive integer factors of 12189 that divides 12189 without a remainder.

1, 3, 17, 51, 239, 717, 4063

Step-4: Factors of 12204

List of positive integer factors of 12204 that divides 12189 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 113, 226, 339, 452, 678, 1017, 1356, 2034, 3051, 4068, 6102

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12189 and 12204. The biggest common factor number is the GCF number.
So the greatest common factor 12189 and 12204 is 3.

Also check out the Least Common Multiple of 12189 and 12204