# Factors of 819

Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, and 819

#### How to find factors of a number

 1.   Find factors of 819 using Division Method 2.   Find factors of 819 using Prime Factorization 3.   Find factors of 819 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 819

• Divide 819 by 1: 819 ÷ 1 : Remainder = 0
• Divide 819 by 3: 819 ÷ 3 : Remainder = 0
• Divide 819 by 7: 819 ÷ 7 : Remainder = 0
• Divide 819 by 9: 819 ÷ 9 : Remainder = 0
• Divide 819 by 13: 819 ÷ 13 : Remainder = 0
• Divide 819 by 21: 819 ÷ 21 : Remainder = 0
• Divide 819 by 39: 819 ÷ 39 : Remainder = 0
• Divide 819 by 63: 819 ÷ 63 : Remainder = 0
• Divide 819 by 91: 819 ÷ 91 : Remainder = 0
• Divide 819 by 117: 819 ÷ 117 : Remainder = 0
• Divide 819 by 273: 819 ÷ 273 : Remainder = 0
• Divide 819 by 819: 819 ÷ 819 : Remainder = 0

Hence, Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, and 819

#### 2. Steps to find factors of 819 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 819 using the division method, follow these steps:

• Step 1. Start dividing 819 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 819, which is 3. Divide 819 by 3 to obtain the quotient (273).
819 ÷ 3 = 273
• Step 3. Repeat step 1 with the obtained quotient (273).
273 ÷ 3 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1

So, the prime factorization of 819 is, 819 = 3 x 3 x 7 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 819 as shown below:

So, the prime factorization of 819 is, 819 = 3 x 3 x 7 x 13.

#### 3. Find factors of 819 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 819 would be the two numbers which, when multiplied, give 819 as the result.

The following table represents the calculation of factors of 819 in pairs:

Factor Pair Pair Factorization
1 and 819 1 x 819 = 819
3 and 273 3 x 273 = 819
7 and 117 7 x 117 = 819
9 and 91 9 x 91 = 819
13 and 63 13 x 63 = 819
21 and 39 21 x 39 = 819

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 819. They are called negative pair factors.

Hence, the negative pairs of 819 would be ( -1 , -819 ) , ( -3 , -273 ) , ( -7 , -117 ) , ( -9 , -91 ) , ( -13 , -63 ) and ( -21 , -39 ) .

#### How can we define factors?

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

#### Properties of factors

• Every number is a factor of zero (0), since 819 x 0 = 0.
• 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, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819 are exact divisors of 819.
• Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819. Each factor divides 819 without leaving a remainder.

• Which is the smallest prime factor of 819?

Smallest prime factor of 819 is 3.

• Is 819 a perfect square?

No 819 is not a perfect square.

• What are five multiples of 819?

First five multiples of 819 are 1638, 2457, 3276, 4095, 4914.

• What is prime factorization of 819?

Prime factorization of 819 is 3 x 3 x 7 x 13.

• What are factors of 819?

Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819.

• How do you find factors of a negative number? ( eg. -819 )?

Factors of -819 are -1, -3, -7, -9, -13, -21, -39, -63, -91, -117, -273, -819.

• Is 819 a whole number?

Yes 819 is a whole number.

• Which is greatest factor of 819?

The greatest factor of 819 is 273.

• What are the prime factors of 819?

The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819.
Prime factors of 819 are 3, 3, 7, 13.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 819. Can you help her?

Prime factors of 819 are 3, 3, 7, 13.
Hence, the product of prime factors of 273.

Can you help Rubel to find out the product of the even factors of 819?

Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819.
Even factors of 819 are 0.
Hence, product of even factors of 819 is; 0 = 0.

Joy wants to calculate mean of all the factors of 819. Help him in finding the mean of 819.

Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 819 is 1 + 3 + 7 + 9 + 13 + 21 + 39 + 63 + 91 + 117 + 273 + 819 = 1456.
Hence, the mean of factors of 819 is 1456 ÷ 12 = 121.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 819? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819.
Negative factors are -1, -3, -7, -9, -13, -21, -39, -63, -91, -117, -273, -819.

How many factors are there for 819?

Factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819.
So there are in total 12 factors.

Joey wants to write all the prime factors of 819 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 819 are 3, 3, 7, 13.
So in exponential form it can be written as 32 x 7 x 13.

Kevin has been asked to write 11 factor(s) of 819. Can you predict the answer?

11 factor(s) of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273.