What is the Greatest Common Factor of 14296 and 14304?

Greatest common factor (GCF) of 14296 and 14304 is 8.

GCF(14296,14304) = 8

We will now calculate the prime factors of 14296 and 14304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14296 and 14304.

How to find the GCF of 14296 and 14304?

We will first find the prime factorization of 14296 and 14304. After we will calculate the factors of 14296 and 14304 and find the biggest common factor number .

Step-1: Prime Factorization of 14296

Prime factors of 14296 are 2, 1787. Prime factorization of 14296 in exponential form is:

14296 = 2³ × 1787¹

Step-2: 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-3: Factors of 14296

List of positive integer factors of 14296 that divides 14296 without a remainder.

1, 2, 4, 8, 1787, 3574, 7148

Step-4: Factors of 14304

List of positive integer factors of 14304 that divides 14296 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14296 and 14304. The biggest common factor number is the GCF number.
So the greatest common factor 14296 and 14304 is 8.

Also check out the Least Common Multiple of 14296 and 14304