# Factors of 810

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

#### How to find factors of a number

 1.   Find factors of 810 using Division Method 2.   Find factors of 810 using Prime Factorization 3.   Find factors of 810 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 810

• Divide 810 by 1: 810 ÷ 1 : Remainder = 0
• Divide 810 by 2: 810 ÷ 2 : Remainder = 0
• Divide 810 by 3: 810 ÷ 3 : Remainder = 0
• Divide 810 by 5: 810 ÷ 5 : Remainder = 0
• Divide 810 by 6: 810 ÷ 6 : Remainder = 0
• Divide 810 by 9: 810 ÷ 9 : Remainder = 0
• Divide 810 by 10: 810 ÷ 10 : Remainder = 0
• Divide 810 by 15: 810 ÷ 15 : Remainder = 0
• Divide 810 by 18: 810 ÷ 18 : Remainder = 0
• Divide 810 by 27: 810 ÷ 27 : Remainder = 0
• Divide 810 by 30: 810 ÷ 30 : Remainder = 0
• Divide 810 by 45: 810 ÷ 45 : Remainder = 0
• Divide 810 by 54: 810 ÷ 54 : Remainder = 0
• Divide 810 by 81: 810 ÷ 81 : Remainder = 0
• Divide 810 by 90: 810 ÷ 90 : Remainder = 0
• Divide 810 by 135: 810 ÷ 135 : Remainder = 0
• Divide 810 by 162: 810 ÷ 162 : Remainder = 0
• Divide 810 by 270: 810 ÷ 270 : Remainder = 0
• Divide 810 by 405: 810 ÷ 405 : Remainder = 0
• Divide 810 by 810: 810 ÷ 810 : Remainder = 0

Hence, 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

#### 2. Steps to find factors of 810 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 810 using the division method, follow these steps:

• Step 1. Start dividing 810 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 810, which is 2. Divide 810 by 2 to obtain the quotient (405).
810 ÷ 2 = 405
• Step 3. Repeat step 1 with the obtained quotient (405).
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 810 is, 810 = 2 x 3 x 3 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 810 as shown below:

So, the prime factorization of 810 is, 810 = 2 x 3 x 3 x 3 x 3 x 5.

#### 3. Find factors of 810 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 810 would be the two numbers which, when multiplied, give 810 as the result.

The following table represents the calculation of factors of 810 in pairs:

Factor Pair Pair Factorization
1 and 810 1 x 810 = 810
2 and 405 2 x 405 = 810
3 and 270 3 x 270 = 810
5 and 162 5 x 162 = 810
6 and 135 6 x 135 = 810
9 and 90 9 x 90 = 810
10 and 81 10 x 81 = 810
15 and 54 15 x 54 = 810
18 and 45 18 x 45 = 810
27 and 30 27 x 30 = 810

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 810. They are called negative pair factors.

Hence, the negative pairs of 810 would be ( -1 , -810 ) , ( -2 , -405 ) , ( -3 , -270 ) , ( -5 , -162 ) , ( -6 , -135 ) , ( -9 , -90 ) , ( -10 , -81 ) , ( -15 , -54 ) , ( -18 , -45 ) and ( -27 , -30 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 810 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810 are exact divisors of 810.
• 1 is a factor of every number. Eg. 1 is a factor of 810.
• Every number is a factor of zero (0), since 810 x 0 = 0.

• Which is the smallest prime factor of 810?

Smallest prime factor of 810 is 2.

• Is 810 a perfect square?

No 810 is not a perfect square.

• What are five multiples of 810?

First five multiples of 810 are 1620, 2430, 3240, 4050, 4860.

• What is prime factorization of 810?

Prime factorization of 810 is 2 x 3 x 3 x 3 x 3 x 5.

• What are factors of 810?

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

• How do you find factors of a negative number? ( eg. -810 )?

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

• Is 810 a whole number?

Yes 810 is a whole number.

• Which is greatest factor of 810?

The greatest factor of 810 is 405.

• What are the prime 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, 810.
Prime factors of 810 are 2, 3, 3, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 810. Can you help her?

Prime factors of 810 are 2, 3, 3, 3, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 810?

Factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810.
Even factors of 810 are 2, 6, 10, 18, 30, 54, 90, 162, 270, 810.
Hence, product of even factors of 810 is; 2 x 6 x 10 x 18 x 30 x 54 x 90 x 162 x 270 x 810 = 11157710083200000.

Joy wants to calculate mean of all the factors of 810. Help him in finding the mean of 810.

Factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 810 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 81 + 90 + 135 + 162 + 270 + 405 + 810 = 2178.
Hence, the mean of factors of 810 is 2178 ÷ 20 = 108.90.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 810? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -270, -405, -810.

How many factors are there for 810?

Factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810.
So there are in total 20 factors.

Joey wants to write all the prime factors of 810 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 810 are 2, 3, 3, 3, 3, 5.
So in exponential form it can be written as 2 x 34 x 5.

Kevin has been asked to write 19 factor(s) of 810. Can you predict the answer?

19 factor(s) of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405.