What is the Greatest Common Factor of 306 and 323?

Greatest common factor (GCF) of 306 and 323 is 17.

GCF(306,323) = 17

We will now calculate the prime factors of 306 and 323, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 306 and 323.

How to find the GCF of 306 and 323?

We will first find the prime factorization of 306 and 323. After we will calculate the factors of 306 and 323 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 323

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

323 = 17¹ × 19¹

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 323

List of positive integer factors of 323 that divides 306 without a remainder.

1, 17, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 306 and 323. The biggest common factor number is the GCF number.
So the greatest common factor 306 and 323 is 17.

Also check out the Least Common Multiple of 306 and 323