What is the Greatest Common Factor of 12669 and 12684?

Greatest common factor (GCF) of 12669 and 12684 is 3.

GCF(12669,12684) = 3

We will now calculate the prime factors of 12669 and 12684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12669 and 12684.

How to find the GCF of 12669 and 12684?

We will first find the prime factorization of 12669 and 12684. After we will calculate the factors of 12669 and 12684 and find the biggest common factor number .

Step-1: Prime Factorization of 12669

Prime factors of 12669 are 3, 41, 103. Prime factorization of 12669 in exponential form is:

12669 = 3¹ × 41¹ × 103¹

Step-2: 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-3: Factors of 12669

List of positive integer factors of 12669 that divides 12669 without a remainder.

1, 3, 41, 103, 123, 309, 4223

Step-4: Factors of 12684

List of positive integer factors of 12684 that divides 12669 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12669 and 12684. The biggest common factor number is the GCF number.
So the greatest common factor 12669 and 12684 is 3.

Also check out the Least Common Multiple of 12669 and 12684