What is the Greatest Common Factor of 17616 and 17625?

Greatest common factor (GCF) of 17616 and 17625 is 3.

GCF(17616,17625) = 3

We will now calculate the prime factors of 17616 and 17625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17616 and 17625.

How to find the GCF of 17616 and 17625?

We will first find the prime factorization of 17616 and 17625. After we will calculate the factors of 17616 and 17625 and find the biggest common factor number .

Step-1: Prime Factorization of 17616

Prime factors of 17616 are 2, 3, 367. Prime factorization of 17616 in exponential form is:

17616 = 2⁴ × 3¹ × 367¹

Step-2: Prime Factorization of 17625

Prime factors of 17625 are 3, 5, 47. Prime factorization of 17625 in exponential form is:

17625 = 3¹ × 5³ × 47¹

Step-3: Factors of 17616

List of positive integer factors of 17616 that divides 17616 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 367, 734, 1101, 1468, 2202, 2936, 4404, 5872, 8808

Step-4: Factors of 17625

List of positive integer factors of 17625 that divides 17616 without a remainder.

1, 3, 5, 15, 25, 47, 75, 125, 141, 235, 375, 705, 1175, 3525, 5875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17616 and 17625. The biggest common factor number is the GCF number.
So the greatest common factor 17616 and 17625 is 3.

Also check out the Least Common Multiple of 17616 and 17625