Greatest Common Factor of 1800 and 1806

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 1800, 1806 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1800 and 1806 is 6.

GCF(1800,1806) = 6

GCF of 1800 and 1806

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

GCF of:
and

Greatest Common Factor of 1800 and 1806

GCF of 1800 and 1806 is 6

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 1806


2 1806
3 903
7 301
43 43
1

Prime factors of 1806 are 2,3,7,43. Prime factorization of 1806 in exponential form is:

1806 = 21×31×71×431

∴ So by taking common prime factors GCF of 1800 and 1806 is 6

Greatest Common Factor of 1800 and 1806 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 1806

List of positive integer factors of 1806 that divides 1806 without a remainder.

1,2,3,6,7,14,21,42,43,86,129,258,301,602,903,1806

Greatest Common Factor

We found the factors and prime factorization of 1800 and 1806. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1806 is 6.

Also check out the Least Common Multiple of 1800 and 1806

Properties of GCF 1800 and 1806

(i) The GCF of 1800 and 1806 is associative

GCF of 1800 and 1806 = GCF of 1806 and 1800

Related Greatest Common Factor of 1800

Related Greatest Common Factor of 1806

Frequently Asked Questions on GCF of 1800 and 1806

1. What is the GCF of 1800 and 1806?

Answer: GCF of 1800 and 1806 is 6.

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 1806?

Answer: Factors of 1806 are 1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903, 1806. There are 16 integers that are factors of 1806. The greatest factor of 1806 is 1806.

4. How to Find the GCF of 1800 and 1806?

Answer:

Greatest Common Factor of 1800 and 1806 = 6

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 1806

1806 = 2 x 3 x 7 x 43

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 1800 and 1806 is 6