Greatest Common Factor of 300 and 306

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, 306 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 300 and 306 is 6.

GCF(300,306) = 6

GCF of 300 and 306

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

GCF of:
and

Greatest Common Factor of 300 and 306

GCF of 300 and 306 is 6

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 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

∴ So by taking common prime factors GCF of 300 and 306 is 6

Greatest Common Factor of 300 and 306 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 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

Greatest Common Factor

We found the factors and prime factorization of 300 and 306. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 306 is 6.

Also check out the Least Common Multiple of 300 and 306

Properties of GCF 300 and 306

(i) The GCF of 300 and 306 is associative

GCF of 300 and 306 = GCF of 306 and 300

Related Greatest Common Factor of 300

Related Greatest Common Factor of 306

Frequently Asked Questions on GCF of 300 and 306

1. What is the GCF of 300 and 306?

Answer: GCF of 300 and 306 is 6.

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 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.

4. How to Find the GCF of 300 and 306?

Answer:

Greatest Common Factor of 300 and 306 = 6

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 306

306 = 2 x 3 x 3 x 17

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 300 and 306 is 6