What is the Greatest Common Factor of 17712 and 17724?

Greatest common factor (GCF) of 17712 and 17724 is 12.

GCF(17712,17724) = 12

We will now calculate the prime factors of 17712 and 17724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17712 and 17724.

How to find the GCF of 17712 and 17724?

We will first find the prime factorization of 17712 and 17724. After we will calculate the factors of 17712 and 17724 and find the biggest common factor number .

Step-1: Prime Factorization of 17712

Prime factors of 17712 are 2, 3, 41. Prime factorization of 17712 in exponential form is:

17712 = 2⁴ × 3³ × 41¹

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 17712

List of positive integer factors of 17712 that divides 17712 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 41, 48, 54, 72, 82, 108, 123, 144, 164, 216, 246, 328, 369, 432, 492, 656, 738, 984, 1107, 1476, 1968, 2214, 2952, 4428, 5904, 8856

Step-4: Factors of 17724

List of positive integer factors of 17724 that divides 17712 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 17712 and 17724. The biggest common factor number is the GCF number.
So the greatest common factor 17712 and 17724 is 12.

Also check out the Least Common Multiple of 17712 and 17724