What is the Greatest Common Factor of 309 and 321?

Greatest common factor (GCF) of 309 and 321 is 3.

GCF(309,321) = 3

We will now calculate the prime factors of 309 and 321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 309 and 321.

How to find the GCF of 309 and 321?

We will first find the prime factorization of 309 and 321. After we will calculate the factors of 309 and 321 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 321

Prime factors of 321 are 3, 107. Prime factorization of 321 in exponential form is:

321 = 3¹ × 107¹

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 321

List of positive integer factors of 321 that divides 309 without a remainder.

1, 3, 107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 309 and 321. The biggest common factor number is the GCF number.
So the greatest common factor 309 and 321 is 3.

Also check out the Least Common Multiple of 309 and 321