What is the Greatest Common Factor of 294 and 306?

Greatest common factor (GCF) of 294 and 306 is 6.

GCF(294,306) = 6

We will now calculate the prime factors of 294 and 306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 294 and 306.

How to find the GCF of 294 and 306?

We will first find the prime factorization of 294 and 306. After we will calculate the factors of 294 and 306 and find the biggest common factor number .

Step-1: Prime Factorization of 294

Prime factors of 294 are 2, 3, 7. Prime factorization of 294 in exponential form is:

294 = 2¹ × 3¹ × 7²

Step-2: 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-3: Factors of 294

List of positive integer factors of 294 that divides 294 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147

Step-4: Factors of 306

List of positive integer factors of 306 that divides 294 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 294 and 306. The biggest common factor number is the GCF number.
So the greatest common factor 294 and 306 is 6.

Also check out the Least Common Multiple of 294 and 306