What is the Greatest Common Factor of 17625 and 17645?

Greatest common factor (GCF) of 17625 and 17645 is 5.

GCF(17625,17645) = 5

We will now calculate the prime factors of 17625 and 17645, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17625 and 17645.

How to find the GCF of 17625 and 17645?

We will first find the prime factorization of 17625 and 17645. After we will calculate the factors of 17625 and 17645 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17645

Prime factors of 17645 are 5, 3529. Prime factorization of 17645 in exponential form is:

17645 = 5¹ × 3529¹

Step-3: Factors of 17625

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

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

Step-4: Factors of 17645

List of positive integer factors of 17645 that divides 17625 without a remainder.

1, 5, 3529

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17625 and 17645. The biggest common factor number is the GCF number.
So the greatest common factor 17625 and 17645 is 5.

Also check out the Least Common Multiple of 17625 and 17645