Factors of 819: Prime Factorization, Methods, and Examples

819 has 12 positive and 12 negative factors. By factors of 819, we mean all the integers that completely divide 819. The term complete division means that when 819 is divided by any of its factors, the division process leaves no remainder. 

The concept of factors and factorization is discussed in detail below.

Factors of 819

Here are the factors of number 819.

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

Negative Factors of 819

The negative factors of 819 are similar to its positive aspects, just with a negative sign.

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

Prime Factorization of 819

The prime factorization of 819 is the way of expressing its prime factors in the product form.

Prime Factorization: 3$^2$ x 7 x 13

In this article, we will learn about the factors of 819 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 819?

The factors of 891 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, and 819. These numbers are the factors as they do not leave any remainder when divided by 819.

The factors of 819 are classified as prime numbers and composite numbers. The prime factors of the number 819 can be determined using the prime factorization technique.

How To Find the Factors of 819?

You can find the factors of 819 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 819, create a list containing the numbers that are exactly divisible by 819 with zero remainders. One important thing to note is that 1 and 819 are the 819’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 819 are determined as follows:

\[\dfrac{819}{1} = 819\]

\[\dfrac{819}{3} = 273\]

\[\dfrac{819}{7} = 117\]

\[\dfrac{819}{9} = 91\]

\[\dfrac{819}{13} = 63\]

\[\dfrac{819}{21} = 39\]

\[\dfrac{819}{39} = 21\]

\[\dfrac{819}{63} = 13\]

\[\dfrac{819}{91} = 9\]

\[\dfrac{819}{117} = 7\]

\[\dfrac{819}{273} = 3\]

\[\dfrac{819}{819} = 1\]

Therefore, 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, and 819 are the factors of 819.

Total Number of Factors of 819

For 819, there are 12 positive factors and n negative ones. So in total, there are 12 factors of 819. 

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 819 is given as:

Factorization of 819 is 1 x 3$^2$ x 7 x 13 .

The exponent of 1, 7, and 13 is 1 and the exponent of 3 is 2.

Adding 1 to each and multiplying them together results in 819.

Therefore, the total number of factors of 819 is 24. 12 are positive, and 12 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 819 by Prime Factorization

The number 819 is a composite 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 819 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 819, 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 819 can be expressed as:

819 = 3$^2$ x 7 x 13

Factors of 819 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 819, the factor pairs can be found as:

1 x 819 = 819

 3 x 273 = 819 

7 x 117 = 819 

9 x 91 = 819 

13 x 63 = 819 

21 x 39 = 819 

The possible factor pairs of 819 are given as (1, 819), (3, 273), (7, 117), (9, 91), (13, 63) and (21, 39).

All these numbers in pairs, when multiplied, give 819 as the product.

The negative factor pairs of 819 are given as:

-1 x -819 = 819 

 -3 x -273 = 819 

-7 x -117 = 819 

-9 x -91 = 819 

-13 x -63 = 819 

-21 x -39 = 819

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, -3, -7, -9, -13, -21, -39, -63, -91, -117, -273 ,and -819 are called negative factors of 819.

The list of all the factors of 819, including positive as well as negative numbers, is given below.

Factor list of 819: 1, -1, 3, -3, 7, -7, 9, -9, 13, -13, 21, -21, 39, -39, 63, -63, 91, -91, 117, -117, 273, -273, 819, and -819

Factors of 819 Solved Examples

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

Example 1

How many factors of 819 are there?

Solution

The total number of Factors of 819 is 12.

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

Example 2

Find the factors of 819 using prime factorization.

Solution

The prime factorization of 819 is given as:

819 $\div$ 3 = 273 

273 $\div$ 3 = 91 

91 $\div$ 7 = 13 

13 $\div$ 13 = 1 

So the prime factorization of 819 can be written as:

3$^2$ x 7 x 13 = 819 

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