Greatest Common Factor of 300 and 308

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, 308 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 300 and 308 is 4.

GCF(300,308) = 4

GCF of 300 and 308

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

GCF of:
and

Greatest Common Factor of 300 and 308

GCF of 300 and 308 is 4

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 308


2 308
2 154
7 77
11 11
1

Prime factors of 308 are 2,7,11. Prime factorization of 308 in exponential form is:

308 = 22×71×111

∴ So by taking common prime factors GCF of 300 and 308 is 4

Greatest Common Factor of 300 and 308 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 308

List of positive integer factors of 308 that divides 308 without a remainder.

1,2,4,7,11,14,22,28,44,77,154,308

Greatest Common Factor

We found the factors and prime factorization of 300 and 308. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 308 is 4.

Also check out the Least Common Multiple of 300 and 308

Properties of GCF 300 and 308

(i) The GCF of 300 and 308 is associative

GCF of 300 and 308 = GCF of 308 and 300

Related Greatest Common Factor of 300

Related Greatest Common Factor of 308

Frequently Asked Questions on GCF of 300 and 308

1. What is the GCF of 300 and 308?

Answer: GCF of 300 and 308 is 4.

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 308?

Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.

4. How to Find the GCF of 300 and 308?

Answer:

Greatest Common Factor of 300 and 308 = 4

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 308

308 = 2 x 2 x 7 x 11

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 300 and 308 is 4