What is the Greatest Common Factor of 13584 and 13590?

Greatest common factor (GCF) of 13584 and 13590 is 6.

GCF(13584,13590) = 6

We will now calculate the prime factors of 13584 and 13590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13584 and 13590.

How to find the GCF of 13584 and 13590?

We will first find the prime factorization of 13584 and 13590. After we will calculate the factors of 13584 and 13590 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 13590

Prime factors of 13590 are 2, 3, 5, 151. Prime factorization of 13590 in exponential form is:

13590 = 2¹ × 3² × 5¹ × 151¹

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 13590

List of positive integer factors of 13590 that divides 13584 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 151, 302, 453, 755, 906, 1359, 1510, 2265, 2718, 4530, 6795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13584 and 13590. The biggest common factor number is the GCF number.
So the greatest common factor 13584 and 13590 is 6.

Also check out the Least Common Multiple of 13584 and 13590