What is the Greatest Common Factor of 12204 and 12214?

Greatest common factor (GCF) of 12204 and 12214 is 2.

GCF(12204,12214) = 2

We will now calculate the prime factors of 12204 and 12214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12204 and 12214.

How to find the GCF of 12204 and 12214?

We will first find the prime factorization of 12204 and 12214. After we will calculate the factors of 12204 and 12214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12214

Prime factors of 12214 are 2, 31, 197. Prime factorization of 12214 in exponential form is:

12214 = 2¹ × 31¹ × 197¹

Step-3: Factors of 12204

List of positive integer factors of 12204 that divides 12204 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

Step-4: Factors of 12214

List of positive integer factors of 12214 that divides 12204 without a remainder.

1, 2, 31, 62, 197, 394, 6107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12204 and 12214. The biggest common factor number is the GCF number.
So the greatest common factor 12204 and 12214 is 2.

Also check out the Least Common Multiple of 12204 and 12214