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Factors of 814: Prime Factorization, Methods, and Examples

The numbers that leave 0 as a remainder when divided by 814 are considered to be its factors. As a result, the factors of 814 are those that divide it exactly. 

When multiplying two integers to get the given number, the factors may be either positive or negative.

Factors of 814

Here are the factors of number 814.

Factors of 814: 1, 2, 11, 22, 37, 74, 407 and 814

Negative Factors of 814

The negative factors of 814 are similar to their positive aspects, just with a negative sign.

Negative Factors of 814: -1, -2, -11, -22, -37, -74, -407 and -814

Prime Factorization of 814

The prime factorization of 814 is the way of expressing its prime factors in the product form.

Prime Factorization: 21  x 111 x 371

In this article, we will learn about the factors of 814 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 814?

The factors of 814 are1, 2, 11, 22, 37, 74, 407 and 814. These numbers are the factors as they do not leave any remainder when divided by 814.

The factors of 814 are classified as prime numbers and composite numbers. The prime factors of the number 814 can be determined using the prime factorization technique.

How To Find the Factors of 814?

You can find the factors of 814 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 814, create a list containing the numbers that are exactly divisible by 814 with zero remainders. One important thing to note is that 1 and 814 are the 814’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 814 are determined as follows:

\[\dfrac{814}{1} = 814\]

\[\dfrac{814}{2} = 407\]

\[\dfrac{814}{11} = 74\]

\[\dfrac{814}{22} = 37\]

\[\dfrac{814}{37} = 22\]

\[\dfrac{814}{74} = 11\]

\[\dfrac{814}{407} = 2\]

\[\dfrac{814}{814} = 1\]

Therefore, 1, 2, 11, 22, 37, 74, 407, and 814 are the factors of 814.

Total Number of Factors of 814

For 814, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 814. 

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 814 is given as:

Factorization of 814 is 21  x 111 x 371.

The exponent of 2, 11, and 37 is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 814 is 16. 8 is positive, and 8 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 814 by Prime Factorization

The number 814 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 814 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 814, 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 814 can be expressed as:

814 = 21  x 111 x 371

Factors of 814 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 814, the factor pairs can be found as:

1 x 814 = 814

2 x 407 = 814

11 x 74 =814

22 x 37 = 814

The possible factor pairs of 814 are given as (1, 814)  (2, 407), (11, 74), and (22, 37).

All these numbers in pairs, when multiplied, give 814 as the product.

The negative factor pairs of 814 are given as:

-1 x -814 = 814

-a x -b = 814

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, -11, -22, -37, -74, -407 and -814 are called negative factors of 814.

The list of all the factors of 814, including positive as well as negative numbers, is given below.

Factor list of 814: 1,-1, 2,-2, 11,-11, 22,-22, 37,-37, 74,-74, 407,-407 , 814, and -814

Factors of 814 Solved Examples

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

Example 1

How many factors of 814 are there?

Solution

The total number of Factors of 814 is 16.

Factors of 814 are1, 2, 11, 22, 37, 74, 407 and 814.

Example 2

Find the factors of 814 using prime factorization.

Solution

The prime factorization of 814 is given as:

814 $\div$ 2 = 407

407 $\div$ 11 = 37

37 $\div$ 37 = 1 

So the prime factorization of 814 can be written as:

21  x 111 x 371= 814

Factors of 813|Factors List| Factors of 815

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