What is the Greatest Common Factor of 17584 and 17589?

Greatest common factor (GCF) of 17584 and 17589 is 1.

GCF(17584,17589) = 1

We will now calculate the prime factors of 17584 and 17589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17584 and 17589.

How to find the GCF of 17584 and 17589?

We will first find the prime factorization of 17584 and 17589. After we will calculate the factors of 17584 and 17589 and find the biggest common factor number .

Step-1: Prime Factorization of 17584

Prime factors of 17584 are 2, 7, 157. Prime factorization of 17584 in exponential form is:

17584 = 2⁴ × 7¹ × 157¹

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 17584

List of positive integer factors of 17584 that divides 17584 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 157, 314, 628, 1099, 1256, 2198, 2512, 4396, 8792

Step-4: Factors of 17589

List of positive integer factors of 17589 that divides 17584 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 17584 and 17589. The biggest common factor number is the GCF number.
So the greatest common factor 17584 and 17589 is 1.

Also check out the Least Common Multiple of 17584 and 17589