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Factors of 813: Prime Factorization, Methods, and Examples

The number 813 has a total of 8 variables, 4 of which are positive and 4 of which are negative. These eight figures are all integers and may all be found on the number line. 

No matter which of these numbers we divide 813 by, the outcome is always a whole number rather than a fraction or decimal.

Factors of 813

Here are the factors of number 813.

Factors of 813:1, 3, 271, and 813

Negative Factors of 813

The negative factors of 813 are similar to its positive aspects, just with a negative sign.

Negative Factors of 813: -1, -3, -271, and -813

Prime Factorization of 813

The prime factorization of 813 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 271

In this article, we will learn about the factors of 813 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 813?

The factors of 813 are1, 3, 271, and 813. These numbers are the factors as they do not leave any remainder when divided by 813.

The factors of 813 are classified as prime numbers and composite numbers. The prime factors of the number 813 can be determined using the prime factorization technique.

How To Find the Factors of 813?

You can find the factors of 813 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 813, create a list containing the numbers that are exactly divisible by 813 with zero remainders. One important thing to note is that 1 and 813 are the 813’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 813 are determined as follows:

\[\dfrac{813}{1} = 813\]

\[\dfrac{813}{3} = 271\]

\[\dfrac{813}{271} = 3\]

\[\dfrac{813}{813} = 1\]

Therefore, 1, 3, 271, and 813 are the factors of 813.

Total Number of Factors of 813

For 813, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 813. 

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 813 is given as:

Factorization of 813 is 1 x 3 x 271.

The exponent of 1, 3, and 271 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 813 is 8. 4 is positive, and 4 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 813 by Prime Factorization

The number 813 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 813 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 813, 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 813 can be expressed as:

813 = 3 x 271

Factors of 813 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 813, the factor pairs can be found as:

1 x 813 = 813

3 x 271 = 813

The possible factor pairs of 813 are given as (1, 813) and (3,271 ).

All these numbers in pairs, when multiplied, give 813 as the product.

The negative factor pairs of 813 are given as:

-1 x -813 = 813

-3 x -271 = 813

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, -271, and -813 are called negative factors of 813.

The list of all the factors of 813, including positive as well as negative numbers, is given below.

Factor list of 813: 1,-1, 3,-3, 271,-271,  813, and -813

Factors of 813 Solved Examples

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

Example 1

How many factors of 813 are there?

Solution

The total number of Factors of 813 is 8.

Factors of 813 are 1, 3, 271, and 813.

Example 2

Find the factors of 813 using prime factorization.

Solution

The prime factorization of 813 is given as:

813 $\div$ 3= 271

271 $\div$ 271 = 1 

So the prime factorization of 813 can be written as:

3 x 271 = 813

Factors of 812|Factors List| Factors of 814

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