What is the Greatest Common Factor of 12274 and 12288?

Greatest common factor (GCF) of 12274 and 12288 is 2.

GCF(12274,12288) = 2

We will now calculate the prime factors of 12274 and 12288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12274 and 12288.

How to find the GCF of 12274 and 12288?

We will first find the prime factorization of 12274 and 12288. After we will calculate the factors of 12274 and 12288 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12288

Prime factors of 12288 are 2, 3. Prime factorization of 12288 in exponential form is:

12288 = 2¹² × 3¹

Step-3: Factors of 12274

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

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

Step-4: Factors of 12288

List of positive integer factors of 12288 that divides 12274 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12274 and 12288. The biggest common factor number is the GCF number.
So the greatest common factor 12274 and 12288 is 2.

Also check out the Least Common Multiple of 12274 and 12288