What is the Greatest Common Factor of 314 and 319?

Greatest common factor (GCF) of 314 and 319 is 1.

GCF(314,319) = 1

We will now calculate the prime factors of 314 and 319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 314 and 319.

How to find the GCF of 314 and 319?

We will first find the prime factorization of 314 and 319. After we will calculate the factors of 314 and 319 and find the biggest common factor number .

Step-1: Prime Factorization of 314

Prime factors of 314 are 2, 157. Prime factorization of 314 in exponential form is:

314 = 2¹ × 157¹

Step-2: Prime Factorization of 319

Prime factors of 319 are 11, 29. Prime factorization of 319 in exponential form is:

319 = 11¹ × 29¹

Step-3: Factors of 314

List of positive integer factors of 314 that divides 314 without a remainder.

1, 2, 157

Step-4: Factors of 319

List of positive integer factors of 319 that divides 314 without a remainder.

1, 11, 29

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 314 and 319. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 319 is 1.

Also check out the Least Common Multiple of 314 and 319