What is the Greatest Common Factor of 12257 and 12274?

Greatest common factor (GCF) of 12257 and 12274 is 17.

GCF(12257,12274) = 17

We will now calculate the prime factors of 12257 and 12274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12257 and 12274.

How to find the GCF of 12257 and 12274?

We will first find the prime factorization of 12257 and 12274. After we will calculate the factors of 12257 and 12274 and find the biggest common factor number .

Step-1: Prime Factorization of 12257

Prime factors of 12257 are 7, 17, 103. Prime factorization of 12257 in exponential form is:

12257 = 7¹ × 17¹ × 103¹

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 12257

List of positive integer factors of 12257 that divides 12257 without a remainder.

1, 7, 17, 103, 119, 721, 1751

Step-4: Factors of 12274

List of positive integer factors of 12274 that divides 12257 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 12257 and 12274. The biggest common factor number is the GCF number.
So the greatest common factor 12257 and 12274 is 17.

Also check out the Least Common Multiple of 12257 and 12274