What is the Greatest Common Factor of 13260 and 13275?

Greatest common factor (GCF) of 13260 and 13275 is 15.

GCF(13260,13275) = 15

We will now calculate the prime factors of 13260 and 13275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13260 and 13275.

How to find the GCF of 13260 and 13275?

We will first find the prime factorization of 13260 and 13275. After we will calculate the factors of 13260 and 13275 and find the biggest common factor number .

Step-1: Prime Factorization of 13260

Prime factors of 13260 are 2, 3, 5, 13, 17. Prime factorization of 13260 in exponential form is:

13260 = 2² × 3¹ × 5¹ × 13¹ × 17¹

Step-2: Prime Factorization of 13275

Prime factors of 13275 are 3, 5, 59. Prime factorization of 13275 in exponential form is:

13275 = 3² × 5² × 59¹

Step-3: Factors of 13260

List of positive integer factors of 13260 that divides 13260 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 17, 20, 26, 30, 34, 39, 51, 52, 60, 65, 68, 78, 85, 102, 130, 156, 170, 195, 204, 221, 255, 260, 340, 390, 442, 510, 663, 780, 884, 1020, 1105, 1326, 2210, 2652, 3315, 4420, 6630

Step-4: Factors of 13275

List of positive integer factors of 13275 that divides 13260 without a remainder.

1, 3, 5, 9, 15, 25, 45, 59, 75, 177, 225, 295, 531, 885, 1475, 2655, 4425

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13260 and 13275. The biggest common factor number is the GCF number.
So the greatest common factor 13260 and 13275 is 15.

Also check out the Least Common Multiple of 13260 and 13275