What is the Greatest Common Factor of 21684 and 21689?

Greatest common factor (GCF) of 21684 and 21689 is 1.

GCF(21684,21689) = 1

We will now calculate the prime factors of 21684 and 21689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21684 and 21689.

How to find the GCF of 21684 and 21689?

We will first find the prime factorization of 21684 and 21689. After we will calculate the factors of 21684 and 21689 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 21689

Prime factors of 21689 are 23, 41. Prime factorization of 21689 in exponential form is:

21689 = 23² × 41¹

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 21689

List of positive integer factors of 21689 that divides 21684 without a remainder.

1, 23, 41, 529, 943

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21684 and 21689. The biggest common factor number is the GCF number.
So the greatest common factor 21684 and 21689 is 1.

Also check out the Least Common Multiple of 21684 and 21689