What is the Greatest Common Factor of 330 and 345?

Greatest common factor (GCF) of 330 and 345 is 15.

GCF(330,345) = 15

We will now calculate the prime factors of 330 and 345, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 330 and 345.

How to find the GCF of 330 and 345?

We will first find the prime factorization of 330 and 345. After we will calculate the factors of 330 and 345 and find the biggest common factor number .

Step-1: Prime Factorization of 330

Prime factors of 330 are 2, 3, 5, 11. Prime factorization of 330 in exponential form is:

330 = 2¹ × 3¹ × 5¹ × 11¹

Step-2: Prime Factorization of 345

Prime factors of 345 are 3, 5, 23. Prime factorization of 345 in exponential form is:

345 = 3¹ × 5¹ × 23¹

Step-3: Factors of 330

List of positive integer factors of 330 that divides 330 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165

Step-4: Factors of 345

List of positive integer factors of 345 that divides 330 without a remainder.

1, 3, 5, 15, 23, 69, 115

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 330 and 345. The biggest common factor number is the GCF number.
So the greatest common factor 330 and 345 is 15.

Also check out the Least Common Multiple of 330 and 345