What is the Greatest Common Factor of 21709 and 21726?

Greatest common factor (GCF) of 21709 and 21726 is 17.

GCF(21709,21726) = 17

We will now calculate the prime factors of 21709 and 21726, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21709 and 21726.

How to find the GCF of 21709 and 21726?

We will first find the prime factorization of 21709 and 21726. After we will calculate the factors of 21709 and 21726 and find the biggest common factor number .

Step-1: Prime Factorization of 21709

Prime factors of 21709 are 17, 1277. Prime factorization of 21709 in exponential form is:

21709 = 17¹ × 1277¹

Step-2: Prime Factorization of 21726

Prime factors of 21726 are 2, 3, 17, 71. Prime factorization of 21726 in exponential form is:

21726 = 2¹ × 3² × 17¹ × 71¹

Step-3: Factors of 21709

List of positive integer factors of 21709 that divides 21709 without a remainder.

1, 17, 1277

Step-4: Factors of 21726

List of positive integer factors of 21726 that divides 21709 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 71, 102, 142, 153, 213, 306, 426, 639, 1207, 1278, 2414, 3621, 7242, 10863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21709 and 21726. The biggest common factor number is the GCF number.
So the greatest common factor 21709 and 21726 is 17.

Also check out the Least Common Multiple of 21709 and 21726