What is the Greatest Common Factor of 14304 and 14315?

Greatest common factor (GCF) of 14304 and 14315 is 1.

GCF(14304,14315) = 1

We will now calculate the prime factors of 14304 and 14315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14304 and 14315.

How to find the GCF of 14304 and 14315?

We will first find the prime factorization of 14304 and 14315. After we will calculate the factors of 14304 and 14315 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 14315

Prime factors of 14315 are 5, 7, 409. Prime factorization of 14315 in exponential form is:

14315 = 5¹ × 7¹ × 409¹

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 14315

List of positive integer factors of 14315 that divides 14304 without a remainder.

1, 5, 7, 35, 409, 2045, 2863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14304 and 14315. The biggest common factor number is the GCF number.
So the greatest common factor 14304 and 14315 is 1.

Also check out the Least Common Multiple of 14304 and 14315