# Greatest Common Factor of 1800 and 1802

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1800, 1802 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1800 and 1802 is 2.

GCF(1800,1802) = 2

## GCF of 1800 and 1802

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

GCF of:
and

### Greatest Common Factor of 1800 and 1802 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 1802

 2 1802 17 901 53 53 1

Prime factors of 1802 are 2,17,53. Prime factorization of 1802 in exponential form is:

1802 = 21×171×531

∴ So by taking common prime factors GCF of 1800 and 1802 is 2

### Greatest Common Factor of 1800 and 1802 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 1802

List of positive integer factors of 1802 that divides 1802 without a remainder.

1,2,17,34,53,106,901,1802

Greatest Common Factor

We found the factors and prime factorization of 1800 and 1802. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1802 is 2.

Also check out the Least Common Multiple of 1800 and 1802

### Properties of GCF 1800 and 1802

(i) The GCF of 1800 and 1802 is associative

GCF of 1800 and 1802 = GCF of 1802 and 1800

### Frequently Asked Questions on GCF of 1800 and 1802

1. What is the GCF of 1800 and 1802?

Answer: GCF of 1800 and 1802 is 2.

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 1802?

Answer: Factors of 1802 are 1, 2, 17, 34, 53, 106, 901, 1802. There are 8 integers that are factors of 1802. The greatest factor of 1802 is 1802.

4. How to Find the GCF of 1800 and 1802?

Greatest Common Factor of 1800 and 1802 = 2

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 1802

1802 = 2 x 17 x 53

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

GCF = 2

Step 4: Therefore, the greatest common factor of 1800 and 1802 is 2