What is the Greatest Common Factor of 13578 and 13584?

Greatest common factor (GCF) of 13578 and 13584 is 6.

GCF(13578,13584) = 6

We will now calculate the prime factors of 13578 and 13584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13578 and 13584.

How to find the GCF of 13578 and 13584?

We will first find the prime factorization of 13578 and 13584. After we will calculate the factors of 13578 and 13584 and find the biggest common factor number .

Step-1: Prime Factorization of 13578

Prime factors of 13578 are 2, 3, 31, 73. Prime factorization of 13578 in exponential form is:

13578 = 2¹ × 3¹ × 31¹ × 73¹

Step-2: 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-3: Factors of 13578

List of positive integer factors of 13578 that divides 13578 without a remainder.

1, 2, 3, 6, 31, 62, 73, 93, 146, 186, 219, 438, 2263, 4526, 6789

Step-4: Factors of 13584

List of positive integer factors of 13584 that divides 13578 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13578 and 13584. The biggest common factor number is the GCF number.
So the greatest common factor 13578 and 13584 is 6.

Also check out the Least Common Multiple of 13578 and 13584