Greatest Common Factor of 306 and 310

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 306, 310 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 306 and 310 is 2.

GCF(306,310) = 2

GCF of 306 and 310

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

GCF of:
and

Greatest Common Factor of 306 and 310

GCF of 306 and 310 is 2

Prime Factorization of 306


2 306
3 153
3 51
17 17
1

Prime factors of 306 are 2,3,17. Prime factorization of 306 in exponential form is:

306 = 21×32×171

Prime Factorization of 310


2 310
5 155
31 31
1

Prime factors of 310 are 2,5,31. Prime factorization of 310 in exponential form is:

310 = 21×51×311

∴ So by taking common prime factors GCF of 306 and 310 is 2

Greatest Common Factor of 306 and 310 by matching factors method

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1,2,3,6,9,17,18,34,51,102,153,306

Factors of 310

List of positive integer factors of 310 that divides 310 without a remainder.

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors and prime factorization of 306 and 310. The biggest common factor number is the GCF number.
So the greatest common factor 306 and 310 is 2.

Also check out the Least Common Multiple of 306 and 310

Properties of GCF 306 and 310

(i) The GCF of 306 and 310 is associative

GCF of 306 and 310 = GCF of 310 and 306

Related Greatest Common Factor of 306

Related Greatest Common Factor of 310

Frequently Asked Questions on GCF of 306 and 310

1. What is the GCF of 306 and 310?

Answer: GCF of 306 and 310 is 2.

2. What are the Factors of 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

3. What are the Factors of 310?

Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.

4. How to Find the GCF of 306 and 310?

Answer:

Greatest Common Factor of 306 and 310 = 2

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 310

310 = 2 x 5 x 31

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

GCF = 2

Step 4: Therefore, the greatest common factor of 306 and 310 is 2