What is the Greatest Common Factor of 17709 and 17724?

Greatest common factor (GCF) of 17709 and 17724 is 3.

GCF(17709,17724) = 3

We will now calculate the prime factors of 17709 and 17724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17709 and 17724.

How to find the GCF of 17709 and 17724?

We will first find the prime factorization of 17709 and 17724. After we will calculate the factors of 17709 and 17724 and find the biggest common factor number .

Step-1: Prime Factorization of 17709

Prime factors of 17709 are 3, 5903. Prime factorization of 17709 in exponential form is:

17709 = 3¹ × 5903¹

Step-2: Prime Factorization of 17724

Prime factors of 17724 are 2, 3, 7, 211. Prime factorization of 17724 in exponential form is:

17724 = 2² × 3¹ × 7¹ × 211¹

Step-3: Factors of 17709

List of positive integer factors of 17709 that divides 17709 without a remainder.

1, 3, 5903

Step-4: Factors of 17724

List of positive integer factors of 17724 that divides 17709 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 211, 422, 633, 844, 1266, 1477, 2532, 2954, 4431, 5908, 8862

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17709 and 17724. The biggest common factor number is the GCF number.
So the greatest common factor 17709 and 17724 is 3.

Also check out the Least Common Multiple of 17709 and 17724