Greatest Common Factor of 304 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 304, 312 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 304 and 312 is 8.

GCF(304,312) = 8

GCF of 304 and 312

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

GCF of:
and

Greatest Common Factor of 304 and 312

GCF of 304 and 312 is 8

Prime Factorization of 304


2 304
2 152
2 76
2 38
19 19
1

Prime factors of 304 are 2,19. Prime factorization of 304 in exponential form is:

304 = 24×191

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 304 and 312 is 8

Greatest Common Factor of 304 and 312 by matching factors method

Factors of 304

List of positive integer factors of 304 that divides 304 without a remainder.

1,2,4,8,16,19,38,76,152,304

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 304 and 312. The biggest common factor number is the GCF number.
So the greatest common factor 304 and 312 is 8.

Also check out the Least Common Multiple of 304 and 312

Properties of GCF 304 and 312

(i) The GCF of 304 and 312 is associative

GCF of 304 and 312 = GCF of 312 and 304

Related Greatest Common Factor of 304

Related Greatest Common Factor of 312

Frequently Asked Questions on GCF of 304 and 312

1. What is the GCF of 304 and 312?

Answer: GCF of 304 and 312 is 8.

2. What are the Factors of 304?

Answer: Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304. There are 10 integers that are factors of 304. The greatest factor of 304 is 304.

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 304 and 312?

Answer:

Greatest Common Factor of 304 and 312 = 8

Step 1: Find the prime factorization of 304

304 = 2 x 2 x 2 x 2 x 19

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 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 304 and 312 is 8