What is the Greatest Common Factor of 314 and 320?

Greatest common factor (GCF) of 314 and 320 is 2.

GCF(314,320) = 2

We will now calculate the prime factors of 314 and 320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 314 and 320.

How to find the GCF of 314 and 320?

We will first find the prime factorization of 314 and 320. After we will calculate the factors of 314 and 320 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 320

Prime factors of 320 are 2, 5. Prime factorization of 320 in exponential form is:

320 = 2⁶ × 5¹

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 320

List of positive integer factors of 320 that divides 314 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 314 and 320. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 320 is 2.

Also check out the Least Common Multiple of 314 and 320