What is the Greatest Common Factor of 13500 and 13504?

Greatest common factor (GCF) of 13500 and 13504 is 4.

GCF(13500,13504) = 4

We will now calculate the prime factors of 13500 and 13504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13500 and 13504.

How to find the GCF of 13500 and 13504?

We will first find the prime factorization of 13500 and 13504. After we will calculate the factors of 13500 and 13504 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13504

Prime factors of 13504 are 2, 211. Prime factorization of 13504 in exponential form is:

13504 = 2⁶ × 211¹

Step-3: Factors of 13500

List of positive integer factors of 13500 that divides 13500 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

Step-4: Factors of 13504

List of positive integer factors of 13504 that divides 13500 without a remainder.

1, 2, 4, 8, 16, 32, 64, 211, 422, 844, 1688, 3376, 6752

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13500 and 13504. The biggest common factor number is the GCF number.
So the greatest common factor 13500 and 13504 is 4.

Also check out the Least Common Multiple of 13500 and 13504