What is the Greatest Common Factor of 17585 and 17590?

Greatest common factor (GCF) of 17585 and 17590 is 5.

GCF(17585,17590) = 5

We will now calculate the prime factors of 17585 and 17590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17585 and 17590.

How to find the GCF of 17585 and 17590?

We will first find the prime factorization of 17585 and 17590. After we will calculate the factors of 17585 and 17590 and find the biggest common factor number .

Step-1: Prime Factorization of 17585

Prime factors of 17585 are 5, 3517. Prime factorization of 17585 in exponential form is:

17585 = 5¹ × 3517¹

Step-2: Prime Factorization of 17590

Prime factors of 17590 are 2, 5, 1759. Prime factorization of 17590 in exponential form is:

17590 = 2¹ × 5¹ × 1759¹

Step-3: Factors of 17585

List of positive integer factors of 17585 that divides 17585 without a remainder.

1, 5, 3517

Step-4: Factors of 17590

List of positive integer factors of 17590 that divides 17585 without a remainder.

1, 2, 5, 10, 1759, 3518, 8795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17585 and 17590. The biggest common factor number is the GCF number.
So the greatest common factor 17585 and 17590 is 5.

Also check out the Least Common Multiple of 17585 and 17590