What is the Greatest Common Factor of 306 and 314?

Greatest common factor (GCF) of 306 and 314 is 2.

GCF(306,314) = 2

We will now calculate the prime factors of 306 and 314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 306 and 314.

How to find the GCF of 306 and 314?

We will first find the prime factorization of 306 and 314. After we will calculate the factors of 306 and 314 and find the biggest common factor number .

Step-1: Prime Factorization of 306

Prime factors of 306 are 2, 3, 17. Prime factorization of 306 in exponential form is:

306 = 2¹ × 3² × 17¹

Step-2: Prime Factorization of 314

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

314 = 2¹ × 157¹

Step-3: Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153

Step-4: Factors of 314

List of positive integer factors of 314 that divides 306 without a remainder.

1, 2, 157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 306 and 314. The biggest common factor number is the GCF number.
So the greatest common factor 306 and 314 is 2.

Also check out the Least Common Multiple of 306 and 314