What is the Greatest Common Factor of 21675 and 21684?

Greatest common factor (GCF) of 21675 and 21684 is 3.

GCF(21675,21684) = 3

We will now calculate the prime factors of 21675 and 21684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21675 and 21684.

How to find the GCF of 21675 and 21684?

We will first find the prime factorization of 21675 and 21684. After we will calculate the factors of 21675 and 21684 and find the biggest common factor number .

Step-1: Prime Factorization of 21675

Prime factors of 21675 are 3, 5, 17. Prime factorization of 21675 in exponential form is:

21675 = 3¹ × 5² × 17²

Step-2: Prime Factorization of 21684

Prime factors of 21684 are 2, 3, 13, 139. Prime factorization of 21684 in exponential form is:

21684 = 2² × 3¹ × 13¹ × 139¹

Step-3: Factors of 21675

List of positive integer factors of 21675 that divides 21675 without a remainder.

1, 3, 5, 15, 17, 25, 51, 75, 85, 255, 289, 425, 867, 1275, 1445, 4335, 7225

Step-4: Factors of 21684

List of positive integer factors of 21684 that divides 21675 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 139, 156, 278, 417, 556, 834, 1668, 1807, 3614, 5421, 7228, 10842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21675 and 21684. The biggest common factor number is the GCF number.
So the greatest common factor 21675 and 21684 is 3.

Also check out the Least Common Multiple of 21675 and 21684