What is the Greatest Common Factor of 308 and 314?

Greatest common factor (GCF) of 308 and 314 is 2.

GCF(308,314) = 2

We will now calculate the prime factors of 308 and 314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 308 and 314.

How to find the GCF of 308 and 314?

We will first find the prime factorization of 308 and 314. After we will calculate the factors of 308 and 314 and find the biggest common factor number .

Step-1: Prime Factorization of 308

Prime factors of 308 are 2, 7, 11. Prime factorization of 308 in exponential form is:

308 = 2² × 7¹ × 11¹

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 308

List of positive integer factors of 308 that divides 308 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154

Step-4: Factors of 314

List of positive integer factors of 314 that divides 308 without a remainder.

1, 2, 157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 308 and 314. The biggest common factor number is the GCF number.
So the greatest common factor 308 and 314 is 2.

Also check out the Least Common Multiple of 308 and 314