Greatest Common Factor of 300 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 300, 310 i.e. 10 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 300 and 310 is 10.

GCF(300,310) = 10

GCF of 300 and 310

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

GCF of:
and

Greatest Common Factor of 300 and 310

GCF of 300 and 310 is 10

Prime Factorization of 300


2 300
2 150
3 75
5 25
5 5
1

Prime factors of 300 are 2,3,5. Prime factorization of 300 in exponential form is:

300 = 22×31×52

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 300 and 310 is 10

Greatest Common Factor of 300 and 310 by matching factors method

Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

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 300 and 310. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 310 is 10.

Also check out the Least Common Multiple of 300 and 310

Properties of GCF 300 and 310

(i) The GCF of 300 and 310 is associative

GCF of 300 and 310 = GCF of 310 and 300

Related Greatest Common Factor of 300

Related Greatest Common Factor of 310

Frequently Asked Questions on GCF of 300 and 310

1. What is the GCF of 300 and 310?

Answer: GCF of 300 and 310 is 10.

2. What are the Factors of 300?

Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.

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 300 and 310?

Answer:

Greatest Common Factor of 300 and 310 = 10

Step 1: Find the prime factorization of 300

300 = 2 x 2 x 3 x 5 x 5

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 x 5 = 10

Step 4: Therefore, the greatest common factor of 300 and 310 is 10