What is the Greatest Common Factor of 14297 and 14314?

Greatest common factor (GCF) of 14297 and 14314 is 17.

GCF(14297,14314) = 17

We will now calculate the prime factors of 14297 and 14314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14297 and 14314.

How to find the GCF of 14297 and 14314?

We will first find the prime factorization of 14297 and 14314. After we will calculate the factors of 14297 and 14314 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 14314

Prime factors of 14314 are 2, 17, 421. Prime factorization of 14314 in exponential form is:

14314 = 2¹ × 17¹ × 421¹

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 14314

List of positive integer factors of 14314 that divides 14297 without a remainder.

1, 2, 17, 34, 421, 842, 7157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14297 and 14314. The biggest common factor number is the GCF number.
So the greatest common factor 14297 and 14314 is 17.

Also check out the Least Common Multiple of 14297 and 14314