What is the Greatest Common Factor of 13584 and 13599?

Greatest common factor (GCF) of 13584 and 13599 is 3.

GCF(13584,13599) = 3

We will now calculate the prime factors of 13584 and 13599, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13584 and 13599.

How to find the GCF of 13584 and 13599?

We will first find the prime factorization of 13584 and 13599. After we will calculate the factors of 13584 and 13599 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 13599

Prime factors of 13599 are 3, 1511. Prime factorization of 13599 in exponential form is:

13599 = 3² × 1511¹

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 13599

List of positive integer factors of 13599 that divides 13584 without a remainder.

1, 3, 9, 1511, 4533

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13584 and 13599. The biggest common factor number is the GCF number.
So the greatest common factor 13584 and 13599 is 3.

Also check out the Least Common Multiple of 13584 and 13599