What is the Greatest Common Factor of 17724 and 17742?

Greatest common factor (GCF) of 17724 and 17742 is 6.

GCF(17724,17742) = 6

We will now calculate the prime factors of 17724 and 17742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17724 and 17742.

How to find the GCF of 17724 and 17742?

We will first find the prime factorization of 17724 and 17742. After we will calculate the factors of 17724 and 17742 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 17742

Prime factors of 17742 are 2, 3, 2957. Prime factorization of 17742 in exponential form is:

17742 = 2¹ × 3¹ × 2957¹

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 17742

List of positive integer factors of 17742 that divides 17724 without a remainder.

1, 2, 3, 6, 2957, 5914, 8871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17724 and 17742. The biggest common factor number is the GCF number.
So the greatest common factor 17724 and 17742 is 6.

Also check out the Least Common Multiple of 17724 and 17742