What is the Greatest Common Factor of 14297 and 14304?

Greatest common factor (GCF) of 14297 and 14304 is 1.

GCF(14297,14304) = 1

We will now calculate the prime factors of 14297 and 14304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14297 and 14304.

How to find the GCF of 14297 and 14304?

We will first find the prime factorization of 14297 and 14304. After we will calculate the factors of 14297 and 14304 and find the biggest common factor number .

Step-1: Prime Factorization of 14297

Prime factors of 14297 are 17, 29. Prime factorization of 14297 in exponential form is:

14297 = 17¹ × 29²

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 14297

List of positive integer factors of 14297 that divides 14297 without a remainder.

1, 17, 29, 493, 841

Step-4: Factors of 14304

List of positive integer factors of 14304 that divides 14297 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 14297 and 14304. The biggest common factor number is the GCF number.
So the greatest common factor 14297 and 14304 is 1.

Also check out the Least Common Multiple of 14297 and 14304