What is the Greatest Common Factor of 14304 and 14313?

Greatest common factor (GCF) of 14304 and 14313 is 3.

GCF(14304,14313) = 3

We will now calculate the prime factors of 14304 and 14313, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14304 and 14313.

How to find the GCF of 14304 and 14313?

We will first find the prime factorization of 14304 and 14313. After we will calculate the factors of 14304 and 14313 and find the biggest common factor number .

Step-1: Prime Factorization of 14304

Prime factors of 14304 are 2, 3, 149. Prime factorization of 14304 in exponential form is:

14304 = 2⁵ × 3¹ × 149¹

Step-2: Prime Factorization of 14313

Prime factors of 14313 are 3, 13, 367. Prime factorization of 14313 in exponential form is:

14313 = 3¹ × 13¹ × 367¹

Step-3: Factors of 14304

List of positive integer factors of 14304 that divides 14304 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 149, 298, 447, 596, 894, 1192, 1788, 2384, 3576, 4768, 7152

Step-4: Factors of 14313

List of positive integer factors of 14313 that divides 14304 without a remainder.

1, 3, 13, 39, 367, 1101, 4771

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14304 and 14313. The biggest common factor number is the GCF number.
So the greatest common factor 14304 and 14313 is 3.

Also check out the Least Common Multiple of 14304 and 14313