What is the Greatest Common Factor of 309 and 316?

Greatest common factor (GCF) of 309 and 316 is 1.

GCF(309,316) = 1

We will now calculate the prime factors of 309 and 316, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 309 and 316.

How to find the GCF of 309 and 316?

We will first find the prime factorization of 309 and 316. After we will calculate the factors of 309 and 316 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 316

Prime factors of 316 are 2, 79. Prime factorization of 316 in exponential form is:

316 = 2² × 79¹

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 316

List of positive integer factors of 316 that divides 309 without a remainder.

1, 2, 4, 79, 158

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 309 and 316. The biggest common factor number is the GCF number.
So the greatest common factor 309 and 316 is 1.

Also check out the Least Common Multiple of 309 and 316