What is the Greatest Common Factor of 17724 and 17738?

Greatest common factor (GCF) of 17724 and 17738 is 14.

GCF(17724,17738) = 14

We will now calculate the prime factors of 17724 and 17738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17724 and 17738.

How to find the GCF of 17724 and 17738?

We will first find the prime factorization of 17724 and 17738. After we will calculate the factors of 17724 and 17738 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17738

Prime factors of 17738 are 2, 7, 181. Prime factorization of 17738 in exponential form is:

17738 = 2¹ × 7² × 181¹

Step-3: Factors of 17724

List of positive integer factors of 17724 that divides 17724 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

Step-4: Factors of 17738

List of positive integer factors of 17738 that divides 17724 without a remainder.

1, 2, 7, 14, 49, 98, 181, 362, 1267, 2534, 8869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17724 and 17738. The biggest common factor number is the GCF number.
So the greatest common factor 17724 and 17738 is 14.

Also check out the Least Common Multiple of 17724 and 17738