# Greatest Common Factor of 1800 and 1805

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1800, 1805 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1800 and 1805 is 5.

GCF(1800,1805) = 5

## GCF of 1800 and 1805

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

GCF of:
and

### Greatest Common Factor of 1800 and 1805 by Prime factorization method

Prime Factorization of 1800

 2 1800 2 900 2 450 3 225 3 75 5 25 5 5 1

Prime factors of 1800 are 2,3,5. Prime factorization of 1800 in exponential form is:

1800 = 23×32×52

Prime Factorization of 1805

 5 1805 19 361 19 19 1

Prime factors of 1805 are 5,19. Prime factorization of 1805 in exponential form is:

1805 = 51×192

∴ So by taking common prime factors GCF of 1800 and 1805 is 5

### Greatest Common Factor of 1800 and 1805 by matching factors method

Factors of 1800

List of positive integer factors of 1800 that divides 1800 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,18,20,24,25,30,36,40,45,50,60,72,75,90,100,120,150,180,200,225,300,360,450,600,900,1800

Factors of 1805

List of positive integer factors of 1805 that divides 1805 without a remainder.

1,5,19,95,361,1805

Greatest Common Factor

We found the factors and prime factorization of 1800 and 1805. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1805 is 5.

Also check out the Least Common Multiple of 1800 and 1805

### Properties of GCF 1800 and 1805

(i) The GCF of 1800 and 1805 is associative

GCF of 1800 and 1805 = GCF of 1805 and 1800

### Frequently Asked Questions on GCF of 1800 and 1805

1. What is the GCF of 1800 and 1805?

Answer: GCF of 1800 and 1805 is 5.

2. What are the Factors of 1800?

Answer: Factors of 1800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800. There are 36 integers that are factors of 1800. The greatest factor of 1800 is 1800.

3. What are the Factors of 1805?

Answer: Factors of 1805 are 1, 5, 19, 95, 361, 1805. There are 6 integers that are factors of 1805. The greatest factor of 1805 is 1805.

4. How to Find the GCF of 1800 and 1805?

Greatest Common Factor of 1800 and 1805 = 5

Step 1: Find the prime factorization of 1800

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 1805

1805 = 5 x 19 x 19

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 1800 and 1805 is 5