What is the Greatest Common Factor of 17725 and 17730?

Greatest common factor (GCF) of 17725 and 17730 is 5.

GCF(17725,17730) = 5

We will now calculate the prime factors of 17725 and 17730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17725 and 17730.

How to find the GCF of 17725 and 17730?

We will first find the prime factorization of 17725 and 17730. After we will calculate the factors of 17725 and 17730 and find the biggest common factor number .

Step-1: Prime Factorization of 17725

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

17725 = 5² × 709¹

Step-2: Prime Factorization of 17730

Prime factors of 17730 are 2, 3, 5, 197. Prime factorization of 17730 in exponential form is:

17730 = 2¹ × 3² × 5¹ × 197¹

Step-3: Factors of 17725

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

1, 5, 25, 709, 3545

Step-4: Factors of 17730

List of positive integer factors of 17730 that divides 17725 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 197, 394, 591, 985, 1182, 1773, 1970, 2955, 3546, 5910, 8865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17725 and 17730. The biggest common factor number is the GCF number.
So the greatest common factor 17725 and 17730 is 5.

Also check out the Least Common Multiple of 17725 and 17730