What is the Greatest Common Factor of 13500 and 13506?

Greatest common factor (GCF) of 13500 and 13506 is 6.

GCF(13500,13506) = 6

We will now calculate the prime factors of 13500 and 13506, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13500 and 13506.

How to find the GCF of 13500 and 13506?

We will first find the prime factorization of 13500 and 13506. After we will calculate the factors of 13500 and 13506 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 13506

Prime factors of 13506 are 2, 3, 2251. Prime factorization of 13506 in exponential form is:

13506 = 2¹ × 3¹ × 2251¹

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 13506

List of positive integer factors of 13506 that divides 13500 without a remainder.

1, 2, 3, 6, 2251, 4502, 6753

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13500 and 13506. The biggest common factor number is the GCF number.
So the greatest common factor 13500 and 13506 is 6.

Also check out the Least Common Multiple of 13500 and 13506