What is the Greatest Common Factor of 309 and 314?

Greatest common factor (GCF) of 309 and 314 is 1.

GCF(309,314) = 1

We will now calculate the prime factors of 309 and 314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 309 and 314.

How to find the GCF of 309 and 314?

We will first find the prime factorization of 309 and 314. After we will calculate the factors of 309 and 314 and find the biggest common factor number .

Step-1: Prime Factorization of 309

Prime factors of 309 are 3, 103. Prime factorization of 309 in exponential form is:

309 = 3¹ × 103¹

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 309

List of positive integer factors of 309 that divides 309 without a remainder.

1, 3, 103

Step-4: Factors of 314

List of positive integer factors of 314 that divides 309 without a remainder.

1, 2, 157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 309 and 314. The biggest common factor number is the GCF number.
So the greatest common factor 309 and 314 is 1.

Also check out the Least Common Multiple of 309 and 314