Greatest Common Factor of 305 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 305, 312 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 305 and 312 is 1.

GCF(305,312) = 1

GCF of 305 and 312

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

GCF of:
and

Greatest Common Factor of 305 and 312

GCF of 305 and 312 is 1

Prime Factorization of 305


5 305
61 61
1

Prime factors of 305 are 5,61. Prime factorization of 305 in exponential form is:

305 = 51×611

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 305 and 312 is 1

Greatest Common Factor of 305 and 312 by matching factors method

Factors of 305

List of positive integer factors of 305 that divides 305 without a remainder.

1,5,61,305

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 305 and 312. The biggest common factor number is the GCF number.
So the greatest common factor 305 and 312 is 1.

Also check out the Least Common Multiple of 305 and 312

Properties of GCF 305 and 312

(i) The GCF of 305 and 312 is associative

GCF of 305 and 312 = GCF of 312 and 305

Related Greatest Common Factor of 305

Related Greatest Common Factor of 312

Frequently Asked Questions on GCF of 305 and 312

1. What is the GCF of 305 and 312?

Answer: GCF of 305 and 312 is 1.

2. What are the Factors of 305?

Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.

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 305 and 312?

Answer:

Greatest Common Factor of 305 and 312 = 1

Step 1: Find the prime factorization of 305

305 = 5 x 61

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 = = 1

Step 4: Therefore, the greatest common factor of 305 and 312 is 1