What is the Greatest Common Factor of 12864 and 12874?

Greatest common factor (GCF) of 12864 and 12874 is 2.

GCF(12864,12874) = 2

We will now calculate the prime factors of 12864 and 12874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12864 and 12874.

How to find the GCF of 12864 and 12874?

We will first find the prime factorization of 12864 and 12874. After we will calculate the factors of 12864 and 12874 and find the biggest common factor number .

Step-1: Prime Factorization of 12864

Prime factors of 12864 are 2, 3, 67. Prime factorization of 12864 in exponential form is:

12864 = 2⁶ × 3¹ × 67¹

Step-2: Prime Factorization of 12874

Prime factors of 12874 are 2, 41, 157. Prime factorization of 12874 in exponential form is:

12874 = 2¹ × 41¹ × 157¹

Step-3: Factors of 12864

List of positive integer factors of 12864 that divides 12864 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 67, 96, 134, 192, 201, 268, 402, 536, 804, 1072, 1608, 2144, 3216, 4288, 6432

Step-4: Factors of 12874

List of positive integer factors of 12874 that divides 12864 without a remainder.

1, 2, 41, 82, 157, 314, 6437

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12864 and 12874. The biggest common factor number is the GCF number.
So the greatest common factor 12864 and 12874 is 2.

Also check out the Least Common Multiple of 12864 and 12874