Greatest Common Factor of 312 and 315

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 312, 315 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 312 and 315 is 3.

GCF(312,315) = 3

GCF of 312 and 315

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

GCF of:
and

Greatest Common Factor of 312 and 315

GCF of 312 and 315 is 3

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

Prime Factorization of 315


3 315
3 105
5 35
7 7
1

Prime factors of 315 are 3,5,7. Prime factorization of 315 in exponential form is:

315 = 32×51×71

∴ So by taking common prime factors GCF of 312 and 315 is 3

Greatest Common Factor of 312 and 315 by matching factors method

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

Factors of 315

List of positive integer factors of 315 that divides 315 without a remainder.

1,3,5,7,9,15,21,35,45,63,105,315

Greatest Common Factor

We found the factors and prime factorization of 312 and 315. The biggest common factor number is the GCF number.
So the greatest common factor 312 and 315 is 3.

Also check out the Least Common Multiple of 312 and 315

Properties of GCF 312 and 315

(i) The GCF of 312 and 315 is associative

GCF of 312 and 315 = GCF of 315 and 312

Related Greatest Common Factor of 312

Related Greatest Common Factor of 315

Frequently Asked Questions on GCF of 312 and 315

1. What is the GCF of 312 and 315?

Answer: GCF of 312 and 315 is 3.

2. 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.

3. What are the Factors of 315?

Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.

4. How to Find the GCF of 312 and 315?

Answer:

Greatest Common Factor of 312 and 315 = 3

Step 1: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

Step 2: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

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

GCF = 3

Step 4: Therefore, the greatest common factor of 312 and 315 is 3