What is the Greatest Common Factor of 28305 and 28320?

Greatest common factor (GCF) of 28305 and 28320 is 15.

GCF(28305,28320) = 15

We will now calculate the prime factors of 28305 and 28320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28305 and 28320.

How to find the GCF of 28305 and 28320?

We will first find the prime factorization of 28305 and 28320. After we will calculate the factors of 28305 and 28320 and find the biggest common factor number .

Step-1: Prime Factorization of 28305

Prime factors of 28305 are 3, 5, 17, 37. Prime factorization of 28305 in exponential form is:

28305 = 3² × 5¹ × 17¹ × 37¹

Step-2: Prime Factorization of 28320

Prime factors of 28320 are 2, 3, 5, 59. Prime factorization of 28320 in exponential form is:

28320 = 2⁵ × 3¹ × 5¹ × 59¹

Step-3: Factors of 28305

List of positive integer factors of 28305 that divides 28305 without a remainder.

1, 3, 5, 9, 15, 17, 37, 45, 51, 85, 111, 153, 185, 255, 333, 555, 629, 765, 1665, 1887, 3145, 5661, 9435

Step-4: Factors of 28320

List of positive integer factors of 28320 that divides 28305 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 59, 60, 80, 96, 118, 120, 160, 177, 236, 240, 295, 354, 472, 480, 590, 708, 885, 944, 1180, 1416, 1770, 1888, 2360, 2832, 3540, 4720, 5664, 7080, 9440, 14160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28305 and 28320. The biggest common factor number is the GCF number.
So the greatest common factor 28305 and 28320 is 15.

Also check out the Least Common Multiple of 28305 and 28320