What is the Greatest Common Factor of 12684 and 12704?

Greatest common factor (GCF) of 12684 and 12704 is 4.

GCF(12684,12704) = 4

We will now calculate the prime factors of 12684 and 12704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12684 and 12704.

How to find the GCF of 12684 and 12704?

We will first find the prime factorization of 12684 and 12704. After we will calculate the factors of 12684 and 12704 and find the biggest common factor number .

Step-1: Prime Factorization of 12684

Prime factors of 12684 are 2, 3, 7, 151. Prime factorization of 12684 in exponential form is:

12684 = 2² × 3¹ × 7¹ × 151¹

Step-2: Prime Factorization of 12704

Prime factors of 12704 are 2, 397. Prime factorization of 12704 in exponential form is:

12704 = 2⁵ × 397¹

Step-3: Factors of 12684

List of positive integer factors of 12684 that divides 12684 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 151, 302, 453, 604, 906, 1057, 1812, 2114, 3171, 4228, 6342

Step-4: Factors of 12704

List of positive integer factors of 12704 that divides 12684 without a remainder.

1, 2, 4, 8, 16, 32, 397, 794, 1588, 3176, 6352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12684 and 12704. The biggest common factor number is the GCF number.
So the greatest common factor 12684 and 12704 is 4.

Also check out the Least Common Multiple of 12684 and 12704