What is the Greatest Common Factor of 13500 and 13510?

Greatest common factor (GCF) of 13500 and 13510 is 10.

GCF(13500,13510) = 10

We will now calculate the prime factors of 13500 and 13510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13500 and 13510.

How to find the GCF of 13500 and 13510?

We will first find the prime factorization of 13500 and 13510. After we will calculate the factors of 13500 and 13510 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 13510

Prime factors of 13510 are 2, 5, 7, 193. Prime factorization of 13510 in exponential form is:

13510 = 2¹ × 5¹ × 7¹ × 193¹

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 13510

List of positive integer factors of 13510 that divides 13500 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 193, 386, 965, 1351, 1930, 2702, 6755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13500 and 13510. The biggest common factor number is the GCF number.
So the greatest common factor 13500 and 13510 is 10.

Also check out the Least Common Multiple of 13500 and 13510