Greatest Common Factor of 306 and 312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 306, 312 i.e. 6 largest integer by which both the numbers can be divided.

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

GCF(306,312) = 6

GCF of 306 and 312

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 306 and 312

GCF of 306 and 312 is 6

Prime Factorization of 306


2 306
3 153
3 51
17 17
1

Prime factors of 306 are 2,3,17. Prime factorization of 306 in exponential form is:

306 = 21×32×171

Prime Factorization of 312


2 312
2 156
2 78
3 39
13 13
1

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

312 = 23×31×131

∴ So by taking common prime factors GCF of 306 and 312 is 6

Greatest Common Factor of 306 and 312 by matching factors method

Factors of 306

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

1,2,3,6,9,17,18,34,51,102,153,306

Factors of 312

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

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

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

Properties of GCF 306 and 312

(i) The GCF of 306 and 312 is associative

GCF of 306 and 312 = GCF of 312 and 306

Related Greatest Common Factor of 306

Related Greatest Common Factor of 312

Frequently Asked Questions on GCF of 306 and 312

1. What is the GCF of 306 and 312?

Answer: GCF of 306 and 312 is 6.

2. What are the Factors of 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

3. What are the Factors of 312?

Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.

4. How to Find the GCF of 306 and 312?

Answer:

Greatest Common Factor of 306 and 312 = 6

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 306 and 312 is 6