What is the Greatest Common Factor of 17712 and 17725?

Greatest common factor (GCF) of 17712 and 17725 is 1.

GCF(17712,17725) = 1

We will now calculate the prime factors of 17712 and 17725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17712 and 17725.

How to find the GCF of 17712 and 17725?

We will first find the prime factorization of 17712 and 17725. After we will calculate the factors of 17712 and 17725 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 17725

Prime factors of 17725 are 5, 709. Prime factorization of 17725 in exponential form is:

17725 = 5² × 709¹

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 17725

List of positive integer factors of 17725 that divides 17712 without a remainder.

1, 5, 25, 709, 3545

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17712 and 17725. The biggest common factor number is the GCF number.
So the greatest common factor 17712 and 17725 is 1.

Also check out the Least Common Multiple of 17712 and 17725