What is the Greatest Common Factor of 13488 and 13500?

Greatest common factor (GCF) of 13488 and 13500 is 12.

GCF(13488,13500) = 12

We will now calculate the prime factors of 13488 and 13500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13488 and 13500.

How to find the GCF of 13488 and 13500?

We will first find the prime factorization of 13488 and 13500. After we will calculate the factors of 13488 and 13500 and find the biggest common factor number .

Step-1: Prime Factorization of 13488

Prime factors of 13488 are 2, 3, 281. Prime factorization of 13488 in exponential form is:

13488 = 2⁴ × 3¹ × 281¹

Step-2: Prime Factorization of 13500

Prime factors of 13500 are 2, 3, 5. Prime factorization of 13500 in exponential form is:

13500 = 2² × 3³ × 5³

Step-3: Factors of 13488

List of positive integer factors of 13488 that divides 13488 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 281, 562, 843, 1124, 1686, 2248, 3372, 4496, 6744

Step-4: Factors of 13500

List of positive integer factors of 13500 that divides 13488 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 675, 750, 900, 1125, 1350, 1500, 2250, 2700, 3375, 4500, 6750

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13488 and 13500. The biggest common factor number is the GCF number.
So the greatest common factor 13488 and 13500 is 12.

Also check out the Least Common Multiple of 13488 and 13500