Greatest Common Factor of 312 and 319

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, 319 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 312 and 319 is 1.

GCF(312,319) = 1

GCF of 312 and 319

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

GCF of:
and

Greatest Common Factor of 312 and 319

GCF of 312 and 319 is 1

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 319


11 319
29 29
1

Prime factors of 319 are 11,29. Prime factorization of 319 in exponential form is:

319 = 111×291

∴ So by taking common prime factors GCF of 312 and 319 is 1

Greatest Common Factor of 312 and 319 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 319

List of positive integer factors of 319 that divides 319 without a remainder.

1,11,29,319

Greatest Common Factor

We found the factors and prime factorization of 312 and 319. The biggest common factor number is the GCF number.
So the greatest common factor 312 and 319 is 1.

Also check out the Least Common Multiple of 312 and 319

Properties of GCF 312 and 319

(i) The GCF of 312 and 319 is associative

GCF of 312 and 319 = GCF of 319 and 312

Related Greatest Common Factor of 312

Related Greatest Common Factor of 319

Frequently Asked Questions on GCF of 312 and 319

1. What is the GCF of 312 and 319?

Answer: GCF of 312 and 319 is 1.

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 319?

Answer: Factors of 319 are 1, 11, 29, 319. There are 4 integers that are factors of 319. The greatest factor of 319 is 319.

4. How to Find the GCF of 312 and 319?

Answer:

Greatest Common Factor of 312 and 319 = 1

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 319

319 = 11 x 29

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 312 and 319 is 1