What is the Greatest Common Factor of 21684 and 21696?

Greatest common factor (GCF) of 21684 and 21696 is 12.

GCF(21684,21696) = 12

We will now calculate the prime factors of 21684 and 21696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21684 and 21696.

How to find the GCF of 21684 and 21696?

We will first find the prime factorization of 21684 and 21696. After we will calculate the factors of 21684 and 21696 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21696

Prime factors of 21696 are 2, 3, 113. Prime factorization of 21696 in exponential form is:

21696 = 2⁶ × 3¹ × 113¹

Step-3: Factors of 21684

List of positive integer factors of 21684 that divides 21684 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

Step-4: Factors of 21696

List of positive integer factors of 21696 that divides 21684 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 113, 192, 226, 339, 452, 678, 904, 1356, 1808, 2712, 3616, 5424, 7232, 10848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21684 and 21696. The biggest common factor number is the GCF number.
So the greatest common factor 21684 and 21696 is 12.

Also check out the Least Common Multiple of 21684 and 21696