Greatest Common Factor of 308 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 308, 312 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 308 and 312 is 4.

GCF(308,312) = 4

GCF of 308 and 312

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

GCF of:
and

Greatest Common Factor of 308 and 312

GCF of 308 and 312 is 4

Prime Factorization of 308


2 308
2 154
7 77
11 11
1

Prime factors of 308 are 2,7,11. Prime factorization of 308 in exponential form is:

308 = 22×71×111

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 308 and 312 is 4

Greatest Common Factor of 308 and 312 by matching factors method

Factors of 308

List of positive integer factors of 308 that divides 308 without a remainder.

1,2,4,7,11,14,22,28,44,77,154,308

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 308 and 312. The biggest common factor number is the GCF number.
So the greatest common factor 308 and 312 is 4.

Also check out the Least Common Multiple of 308 and 312

Properties of GCF 308 and 312

(i) The GCF of 308 and 312 is associative

GCF of 308 and 312 = GCF of 312 and 308

Related Greatest Common Factor of 308

Related Greatest Common Factor of 312

Frequently Asked Questions on GCF of 308 and 312

1. What is the GCF of 308 and 312?

Answer: GCF of 308 and 312 is 4.

2. What are the Factors of 308?

Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.

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 308 and 312?

Answer:

Greatest Common Factor of 308 and 312 = 4

Step 1: Find the prime factorization of 308

308 = 2 x 2 x 7 x 11

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 = 4

Step 4: Therefore, the greatest common factor of 308 and 312 is 4