What is the Greatest Common Factor of 13185 and 13200?

Greatest common factor (GCF) of 13185 and 13200 is 15.

GCF(13185,13200) = 15

We will now calculate the prime factors of 13185 and 13200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13185 and 13200.

How to find the GCF of 13185 and 13200?

We will first find the prime factorization of 13185 and 13200. After we will calculate the factors of 13185 and 13200 and find the biggest common factor number .

Step-1: Prime Factorization of 13185

Prime factors of 13185 are 3, 5, 293. Prime factorization of 13185 in exponential form is:

13185 = 3² × 5¹ × 293¹

Step-2: Prime Factorization of 13200

Prime factors of 13200 are 2, 3, 5, 11. Prime factorization of 13200 in exponential form is:

13200 = 2⁴ × 3¹ × 5² × 11¹

Step-3: Factors of 13185

List of positive integer factors of 13185 that divides 13185 without a remainder.

1, 3, 5, 9, 15, 45, 293, 879, 1465, 2637, 4395

Step-4: Factors of 13200

List of positive integer factors of 13200 that divides 13185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 100, 110, 120, 132, 150, 165, 176, 200, 220, 240, 264, 275, 300, 330, 400, 440, 528, 550, 600, 660, 825, 880, 1100, 1200, 1320, 1650, 2200, 2640, 3300, 4400, 6600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13185 and 13200. The biggest common factor number is the GCF number.
So the greatest common factor 13185 and 13200 is 15.

Also check out the Least Common Multiple of 13185 and 13200