What is the Greatest Common Factor of 17265 and 17280?

Greatest common factor (GCF) of 17265 and 17280 is 15.

GCF(17265,17280) = 15

We will now calculate the prime factors of 17265 and 17280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17265 and 17280.

How to find the GCF of 17265 and 17280?

We will first find the prime factorization of 17265 and 17280. After we will calculate the factors of 17265 and 17280 and find the biggest common factor number .

Step-1: Prime Factorization of 17265

Prime factors of 17265 are 3, 5, 1151. Prime factorization of 17265 in exponential form is:

17265 = 3¹ × 5¹ × 1151¹

Step-2: Prime Factorization of 17280

Prime factors of 17280 are 2, 3, 5. Prime factorization of 17280 in exponential form is:

17280 = 2⁷ × 3³ × 5¹

Step-3: Factors of 17265

List of positive integer factors of 17265 that divides 17265 without a remainder.

1, 3, 5, 15, 1151, 3453, 5755

Step-4: Factors of 17280

List of positive integer factors of 17280 that divides 17265 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 128, 135, 144, 160, 180, 192, 216, 240, 270, 288, 320, 360, 384, 432, 480, 540, 576, 640, 720, 864, 960, 1080, 1152, 1440, 1728, 1920, 2160, 2880, 3456, 4320, 5760, 8640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17265 and 17280. The biggest common factor number is the GCF number.
So the greatest common factor 17265 and 17280 is 15.

Also check out the Least Common Multiple of 17265 and 17280