What is the Greatest Common Factor of 17580 and 17589?

Greatest common factor (GCF) of 17580 and 17589 is 3.

GCF(17580,17589) = 3

We will now calculate the prime factors of 17580 and 17589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17580 and 17589.

How to find the GCF of 17580 and 17589?

We will first find the prime factorization of 17580 and 17589. After we will calculate the factors of 17580 and 17589 and find the biggest common factor number .

Step-1: Prime Factorization of 17580

Prime factors of 17580 are 2, 3, 5, 293. Prime factorization of 17580 in exponential form is:

17580 = 2² × 3¹ × 5¹ × 293¹

Step-2: Prime Factorization of 17589

Prime factors of 17589 are 3, 11, 13, 41. Prime factorization of 17589 in exponential form is:

17589 = 3¹ × 11¹ × 13¹ × 41¹

Step-3: Factors of 17580

List of positive integer factors of 17580 that divides 17580 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 293, 586, 879, 1172, 1465, 1758, 2930, 3516, 4395, 5860, 8790

Step-4: Factors of 17589

List of positive integer factors of 17589 that divides 17580 without a remainder.

1, 3, 11, 13, 33, 39, 41, 123, 143, 429, 451, 533, 1353, 1599, 5863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17580 and 17589. The biggest common factor number is the GCF number.
So the greatest common factor 17580 and 17589 is 3.

Also check out the Least Common Multiple of 17580 and 17589