What is the Greatest Common Factor of 13584 and 13589?

Greatest common factor (GCF) of 13584 and 13589 is 1.

GCF(13584,13589) = 1

We will now calculate the prime factors of 13584 and 13589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13584 and 13589.

How to find the GCF of 13584 and 13589?

We will first find the prime factorization of 13584 and 13589. After we will calculate the factors of 13584 and 13589 and find the biggest common factor number .

Step-1: Prime Factorization of 13584

Prime factors of 13584 are 2, 3, 283. Prime factorization of 13584 in exponential form is:

13584 = 2⁴ × 3¹ × 283¹

Step-2: Prime Factorization of 13589

Prime factors of 13589 are 107, 127. Prime factorization of 13589 in exponential form is:

13589 = 107¹ × 127¹

Step-3: Factors of 13584

List of positive integer factors of 13584 that divides 13584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 283, 566, 849, 1132, 1698, 2264, 3396, 4528, 6792

Step-4: Factors of 13589

List of positive integer factors of 13589 that divides 13584 without a remainder.

1, 107, 127

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13584 and 13589. The biggest common factor number is the GCF number.
So the greatest common factor 13584 and 13589 is 1.

Also check out the Least Common Multiple of 13584 and 13589