 # Factors of 810: Prime Factorization, Methods, and Examples

The article includes many techniques for determining the elements of 810. A number that is a multiple of more than two integers is referred to as a composite number. 810 is therefore included in the list of composite numbers. The smallest prime factor of 810, which is even, is 2. There are 20 factors totaling 810

### Factors of 810

Here are the factors of number 810.

Factors of 810: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 and 810

### Negative Factors of 810

The negative factors of 810 are similar to its positive aspects, just with a negative sign.

Negative Factors of 810: -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -270, -405 and-810

### Prime Factorization of 810

The prime factorization of 810 is the way of expressing its prime factors in the product form. Prime Factorization: 21 x 34 x 51

In this article, we will learn about the factors of 810 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 810?

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 and 810. These numbers are the factors as they do not leave any remainder when divided by 810.

The factors of 810 are classified as prime numbers and composite numbers. The prime factors of the number 810 can be determined using the prime factorization technique.

## How To Find the Factors of 810?

You can find the factors of 810 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 810, create a list containing the numbers that are exactly divisible by 810 with zero remainders. One important thing to note is that 1 and 810 are the 810’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 810 are determined as follows:

$\dfrac{810}{1} = 810$

$\dfrac{810}{2} = 405$

$\dfrac{810}{3} = 270$

$\dfrac{810}{5} = 162$

$\dfrac{810}{6} = 135$

$\dfrac{810}{9} = 90$

$\dfrac{810}{10} = 81$

$\dfrac{810}{15} =54$

$\dfrac{810}{18} = 45$

$\dfrac{810}{27} = 30$

$\dfrac{810}{30} = 27$

$\dfrac{810}{45} = 18$

$\dfrac{810}{54} = 15$

$\dfrac{810}{81} = 10$

$\dfrac{810}{90} = 9$

$\dfrac{810}{135} = 6$

$\dfrac{810}{162} = 5$

$\dfrac{810}{270} = 3$

$\dfrac{810}{405} = 2$

$\dfrac{810}{810} = 1$

Therefore, 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 and 810 are the factors of 810.

### Total Number of Factors of 810

For 810, there are 20 positive factors and 20 negative ones. So in total, there are 40 factors of 810.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 810 is given as:

Factorization of 810 is 21 x 34 x 51.

The exponent of 2 is 1,  3 is 4, and 5 is 1.

Adding 1 to each and multiplying them together results in 40.

Therefore, the total number of factors of 810 is 40. 20 are positive, and 20 factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 810 by Prime Factorization

The number 810 is a composite/prime number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 810 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 810, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 810 can be expressed as:

810 = 21 x 34 x 51

## Factors of 810 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given. For 810, the factor pairs can be found as:

1 x 810 = 810

2 x 405 = 810

3 x 270 = 810

5 x 162 = 810

6 x 135 = 810

9 x 90 = 810

10 x 81 = 810

15 x 54 =810

18 x 45 = 810

27 x 30 = 810

The possible factor pairs of 810 are given as (1, 810),(2, 405),(3, 270),(5, 162),(6, 135),(9, 90),(10, 81),(15, 54), (18, 45) and (27, 30).

All these numbers in pairs, when multiplied, give 810 as the product.

The negative factor pairs of 810 are given as:

-1 x -810 = 810

-2 x -405 = 810

-3 x -270 = 810

-5 x -162 = 810

-6 x -135 = 810

-9 x -90 = 810

-10 x -81 = 810

-15 x -54 =810

-18 x -45 = 810

-27 x -30 = 810

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -270, -405 and-810are called negative factors of 810.

The list of all the factors of 810, including positive as well as negative numbers, is given below.

Factor list of 810: 1,-1, 2,-2, 3,-3, 5,-5, 6,-6,9, -9, 10,-10, 15,-15, 18,-18, 27,-27,30, -30, 45,-45, 54,-54, 81,-81, 90,-90, 135,-135, 162,-162, 270,-270, 405,-405, 810, and -810

## Factors of 810 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 810 are there?

### Solution

The total number of Factors of 810 is 40.

Factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 and 810.

### Example 2

Find the factors of 810 using prime factorization.

### Solution

The prime factorization of 810 is given as:

810 $\div$ 2 = 405

405 $\div$ 3 = 135

135 $\div$ 3 =45

45 $\div$ 3 = 15

15 $\div$ 3 = 5

5 $\div$ 5 = 1

So the prime factorization of 810 can be written as:

21 x 34 x 51 = 810