What is the Greatest Common Factor of 300 and 309?

Greatest common factor (GCF) of 300 and 309 is 3.

GCF(300,309) = 3

We will now calculate the prime factors of 300 and 309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 309.

How to find the GCF of 300 and 309?

We will first find the prime factorization of 300 and 309. After we will calculate the factors of 300 and 309 and find the biggest common factor number .

Step-1: Prime Factorization of 300

Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:

300 = 2² × 3¹ × 5²

Step-2: Prime Factorization of 309

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

309 = 3¹ × 103¹

Step-3: Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150

Step-4: Factors of 309

List of positive integer factors of 309 that divides 300 without a remainder.

1, 3, 103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 309. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 309 is 3.

Also check out the Least Common Multiple of 300 and 309