What is the Greatest Common Factor of 21684 and 21697?

Greatest common factor (GCF) of 21684 and 21697 is 13.

GCF(21684,21697) = 13

We will now calculate the prime factors of 21684 and 21697, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21684 and 21697.

How to find the GCF of 21684 and 21697?

We will first find the prime factorization of 21684 and 21697. After we will calculate the factors of 21684 and 21697 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 21697

Prime factors of 21697 are 13, 1669. Prime factorization of 21697 in exponential form is:

21697 = 13¹ × 1669¹

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 21697

List of positive integer factors of 21697 that divides 21684 without a remainder.

1, 13, 1669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21684 and 21697. The biggest common factor number is the GCF number.
So the greatest common factor 21684 and 21697 is 13.

Also check out the Least Common Multiple of 21684 and 21697