What is the Greatest Common Factor of 28305 and 28314?

Greatest common factor (GCF) of 28305 and 28314 is 9.

GCF(28305,28314) = 9

We will now calculate the prime factors of 28305 and 28314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28305 and 28314.

How to find the GCF of 28305 and 28314?

We will first find the prime factorization of 28305 and 28314. After we will calculate the factors of 28305 and 28314 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 28314

Prime factors of 28314 are 2, 3, 11, 13. Prime factorization of 28314 in exponential form is:

28314 = 2¹ × 3² × 11² × 13¹

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 28314

List of positive integer factors of 28314 that divides 28305 without a remainder.

1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 121, 143, 198, 234, 242, 286, 363, 429, 726, 858, 1089, 1287, 1573, 2178, 2574, 3146, 4719, 9438, 14157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28305 and 28314. The biggest common factor number is the GCF number.
So the greatest common factor 28305 and 28314 is 9.

Also check out the Least Common Multiple of 28305 and 28314