Greatest Common Factor of 300 and 305

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, 305 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 300 and 305 is 5.

GCF(300,305) = 5

GCF of 300 and 305

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

GCF of:
and

Greatest Common Factor of 300 and 305

GCF of 300 and 305 is 5

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 305


5 305
61 61
1

Prime factors of 305 are 5,61. Prime factorization of 305 in exponential form is:

305 = 51×611

∴ So by taking common prime factors GCF of 300 and 305 is 5

Greatest Common Factor of 300 and 305 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 305

List of positive integer factors of 305 that divides 305 without a remainder.

1,5,61,305

Greatest Common Factor

We found the factors and prime factorization of 300 and 305. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 305 is 5.

Also check out the Least Common Multiple of 300 and 305

Properties of GCF 300 and 305

(i) The GCF of 300 and 305 is associative

GCF of 300 and 305 = GCF of 305 and 300

Related Greatest Common Factor of 300

Related Greatest Common Factor of 305

Frequently Asked Questions on GCF of 300 and 305

1. What is the GCF of 300 and 305?

Answer: GCF of 300 and 305 is 5.

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 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.

4. How to Find the GCF of 300 and 305?

Answer:

Greatest Common Factor of 300 and 305 = 5

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 305

305 = 5 x 61

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 300 and 305 is 5