What is the Greatest Common Factor of 309 and 323?

Greatest common factor (GCF) of 309 and 323 is 1.

GCF(309,323) = 1

We will now calculate the prime factors of 309 and 323, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 309 and 323.

How to find the GCF of 309 and 323?

We will first find the prime factorization of 309 and 323. After we will calculate the factors of 309 and 323 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 323

Prime factors of 323 are 17, 19. Prime factorization of 323 in exponential form is:

323 = 17¹ × 19¹

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 323

List of positive integer factors of 323 that divides 309 without a remainder.

1, 17, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 309 and 323. The biggest common factor number is the GCF number.
So the greatest common factor 309 and 323 is 1.

Also check out the Least Common Multiple of 309 and 323