What is the Greatest Common Factor of 306 and 312?

Greatest common factor (GCF) of 306 and 312 is 6.

GCF(306,312) = 6

We will now calculate the prime factors of 306 and 312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 306 and 312.

How to find the GCF of 306 and 312?

We will first find the prime factorization of 306 and 312. After we will calculate the factors of 306 and 312 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 312

Prime factors of 312 are 2, 3, 13. Prime factorization of 312 in exponential form is:

312 = 2³ × 3¹ × 13¹

Step-3: Factors of 306

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

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

Step-4: Factors of 312

List of positive integer factors of 312 that divides 306 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 306 and 312. The biggest common factor number is the GCF number.
So the greatest common factor 306 and 312 is 6.

Also check out the Least Common Multiple of 306 and 312