What is the Greatest Common Factor of 14305 and 14310?

Greatest common factor (GCF) of 14305 and 14310 is 5.

GCF(14305,14310) = 5

We will now calculate the prime factors of 14305 and 14310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14305 and 14310.

How to find the GCF of 14305 and 14310?

We will first find the prime factorization of 14305 and 14310. After we will calculate the factors of 14305 and 14310 and find the biggest common factor number .

Step-1: Prime Factorization of 14305

Prime factors of 14305 are 5, 2861. Prime factorization of 14305 in exponential form is:

14305 = 5¹ × 2861¹

Step-2: Prime Factorization of 14310

Prime factors of 14310 are 2, 3, 5, 53. Prime factorization of 14310 in exponential form is:

14310 = 2¹ × 3³ × 5¹ × 53¹

Step-3: Factors of 14305

List of positive integer factors of 14305 that divides 14305 without a remainder.

1, 5, 2861

Step-4: Factors of 14310

List of positive integer factors of 14310 that divides 14305 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 53, 54, 90, 106, 135, 159, 265, 270, 318, 477, 530, 795, 954, 1431, 1590, 2385, 2862, 4770, 7155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14305 and 14310. The biggest common factor number is the GCF number.
So the greatest common factor 14305 and 14310 is 5.

Also check out the Least Common Multiple of 14305 and 14310