What is the Greatest Common Factor of 314 and 333?

Greatest common factor (GCF) of 314 and 333 is 1.

GCF(314,333) = 1

We will now calculate the prime factors of 314 and 333, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 314 and 333.

How to find the GCF of 314 and 333?

We will first find the prime factorization of 314 and 333. After we will calculate the factors of 314 and 333 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 333

Prime factors of 333 are 3, 37. Prime factorization of 333 in exponential form is:

333 = 3² × 37¹

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 333

List of positive integer factors of 333 that divides 314 without a remainder.

1, 3, 9, 37, 111

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 314 and 333. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 333 is 1.

Also check out the Least Common Multiple of 314 and 333