What is the Greatest Common Factor of 294 and 303?

Greatest common factor (GCF) of 294 and 303 is 3.

GCF(294,303) = 3

We will now calculate the prime factors of 294 and 303, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 294 and 303.

How to find the GCF of 294 and 303?

We will first find the prime factorization of 294 and 303. After we will calculate the factors of 294 and 303 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 303

Prime factors of 303 are 3, 101. Prime factorization of 303 in exponential form is:

303 = 3¹ × 101¹

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 303

List of positive integer factors of 303 that divides 294 without a remainder.

1, 3, 101

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 294 and 303. The biggest common factor number is the GCF number.
So the greatest common factor 294 and 303 is 3.

Also check out the Least Common Multiple of 294 and 303