What is the Greatest Common Factor of 13500 and 13509?

Greatest common factor (GCF) of 13500 and 13509 is 9.

GCF(13500,13509) = 9

We will now calculate the prime factors of 13500 and 13509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13500 and 13509.

How to find the GCF of 13500 and 13509?

We will first find the prime factorization of 13500 and 13509. After we will calculate the factors of 13500 and 13509 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 13509

Prime factors of 13509 are 3, 19, 79. Prime factorization of 13509 in exponential form is:

13509 = 3² × 19¹ × 79¹

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 13509

List of positive integer factors of 13509 that divides 13500 without a remainder.

1, 3, 9, 19, 57, 79, 171, 237, 711, 1501, 4503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13500 and 13509. The biggest common factor number is the GCF number.
So the greatest common factor 13500 and 13509 is 9.

Also check out the Least Common Multiple of 13500 and 13509