What is the Greatest Common Factor of 314 and 330?

Greatest common factor (GCF) of 314 and 330 is 2.

GCF(314,330) = 2

We will now calculate the prime factors of 314 and 330, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 314 and 330.

How to find the GCF of 314 and 330?

We will first find the prime factorization of 314 and 330. After we will calculate the factors of 314 and 330 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 330

Prime factors of 330 are 2, 3, 5, 11. Prime factorization of 330 in exponential form is:

330 = 2¹ × 3¹ × 5¹ × 11¹

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 330

List of positive integer factors of 330 that divides 314 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 314 and 330. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 330 is 2.

Also check out the Least Common Multiple of 314 and 330