What is the Greatest Common Factor of 13500 and 13519?

Greatest common factor (GCF) of 13500 and 13519 is 1.

GCF(13500,13519) = 1

We will now calculate the prime factors of 13500 and 13519, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13500 and 13519.

How to find the GCF of 13500 and 13519?

We will first find the prime factorization of 13500 and 13519. After we will calculate the factors of 13500 and 13519 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 13519

Prime factors of 13519 are 11, 1229. Prime factorization of 13519 in exponential form is:

13519 = 11¹ × 1229¹

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 13519

List of positive integer factors of 13519 that divides 13500 without a remainder.

1, 11, 1229

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13500 and 13519. The biggest common factor number is the GCF number.
So the greatest common factor 13500 and 13519 is 1.

Also check out the Least Common Multiple of 13500 and 13519