Greatest Common Factor of 305 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 305, 310 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 305 and 310 is 5.

GCF(305,310) = 5

GCF of 305 and 310

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

GCF of:
and

Greatest Common Factor of 305 and 310

GCF of 305 and 310 is 5

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 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 305 and 310 is 5

Greatest Common Factor of 305 and 310 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 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 305 and 310. The biggest common factor number is the GCF number.
So the greatest common factor 305 and 310 is 5.

Also check out the Least Common Multiple of 305 and 310

Properties of GCF 305 and 310

(i) The GCF of 305 and 310 is associative

GCF of 305 and 310 = GCF of 310 and 305

Related Greatest Common Factor of 305

Related Greatest Common Factor of 310

Frequently Asked Questions on GCF of 305 and 310

1. What is the GCF of 305 and 310?

Answer: GCF of 305 and 310 is 5.

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 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 305 and 310?

Answer:

Greatest Common Factor of 305 and 310 = 5

Step 1: Find the prime factorization of 305

305 = 5 x 61

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 = 5

Step 4: Therefore, the greatest common factor of 305 and 310 is 5