What is the Greatest Common Factor of 14304 and 14320?

Greatest common factor (GCF) of 14304 and 14320 is 16.

GCF(14304,14320) = 16

We will now calculate the prime factors of 14304 and 14320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14304 and 14320.

How to find the GCF of 14304 and 14320?

We will first find the prime factorization of 14304 and 14320. After we will calculate the factors of 14304 and 14320 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 14320

Prime factors of 14320 are 2, 5, 179. Prime factorization of 14320 in exponential form is:

14320 = 2⁴ × 5¹ × 179¹

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 14320

List of positive integer factors of 14320 that divides 14304 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 179, 358, 716, 895, 1432, 1790, 2864, 3580, 7160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14304 and 14320. The biggest common factor number is the GCF number.
So the greatest common factor 14304 and 14320 is 16.

Also check out the Least Common Multiple of 14304 and 14320