What is the Greatest Common Factor of 12258 and 12274?

Greatest common factor (GCF) of 12258 and 12274 is 2.

GCF(12258,12274) = 2

We will now calculate the prime factors of 12258 and 12274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12258 and 12274.

How to find the GCF of 12258 and 12274?

We will first find the prime factorization of 12258 and 12274. After we will calculate the factors of 12258 and 12274 and find the biggest common factor number .

Step-1: Prime Factorization of 12258

Prime factors of 12258 are 2, 3, 227. Prime factorization of 12258 in exponential form is:

12258 = 2¹ × 3³ × 227¹

Step-2: Prime Factorization of 12274

Prime factors of 12274 are 2, 17, 19. Prime factorization of 12274 in exponential form is:

12274 = 2¹ × 17¹ × 19²

Step-3: Factors of 12258

List of positive integer factors of 12258 that divides 12258 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 227, 454, 681, 1362, 2043, 4086, 6129

Step-4: Factors of 12274

List of positive integer factors of 12274 that divides 12258 without a remainder.

1, 2, 17, 19, 34, 38, 323, 361, 646, 722, 6137

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12258 and 12274. The biggest common factor number is the GCF number.
So the greatest common factor 12258 and 12274 is 2.

Also check out the Least Common Multiple of 12258 and 12274