What is the Greatest Common Factor of 17280 and 17289?

Greatest common factor (GCF) of 17280 and 17289 is 9.

GCF(17280,17289) = 9

We will now calculate the prime factors of 17280 and 17289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17280 and 17289.

How to find the GCF of 17280 and 17289?

We will first find the prime factorization of 17280 and 17289. After we will calculate the factors of 17280 and 17289 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17289

Prime factors of 17289 are 3, 17, 113. Prime factorization of 17289 in exponential form is:

17289 = 3² × 17¹ × 113¹

Step-3: Factors of 17280

List of positive integer factors of 17280 that divides 17280 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

Step-4: Factors of 17289

List of positive integer factors of 17289 that divides 17280 without a remainder.

1, 3, 9, 17, 51, 113, 153, 339, 1017, 1921, 5763

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17280 and 17289. The biggest common factor number is the GCF number.
So the greatest common factor 17280 and 17289 is 9.

Also check out the Least Common Multiple of 17280 and 17289