Factors of 821: Prime Factorization, Methods, and Examples

821 is a prime number which means that it has only two factors that are 1 and 821 itself. As 821 is a prime number so there is no such number other than 1 and 821 that give 0 as a remainder when 821 is divided by it.

Factors Of 821

 Further details are given in the article below.

Factors of 821

Here are the factors of number 821.

Factors of 821: 1 and 821

Negative Factors of 821

The negative factors of 821 are similar to its positive aspects, just with a negative sign.

Negative Factors of 821: – 1 and -821

Prime Factorization of 821

The prime factorization of 821 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 821

In this article, we will learn about the factors of 821 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 821?

The factors of 821 are 1 and 821. These numbers are the factors as they do not leave any remainder when divided by 821.

The factors of 821 are classified as prime numbers and composite numbers. The prime factors of the number 821 can be determined using the prime factorization technique.

How To Find the Factors of 821?

You can find the factors of 821 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 821, create a list containing the numbers that are exactly divisible by 821 with zero remainders. One important thing to note is that 1 and 821 are the 821’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 821 are determined as follows:

\[\dfrac{821}{1} = 821\]

\[\dfrac{821}{821} = 1\]

Therefore, 1 and 821 are the factors of 821.

Total Number of Factors of 821

For 821, there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 821. 

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 821 is given as:

Factorization of 821 is 1 x 821.

The exponent of 1 and 821 is 1.

Adding 1 to each and multiplying them together results in 821.

Therefore, the total number of factors of 821 is 4. 2 are positive, and 2 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 821 by Prime Factorization

The number 821 is a prime 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.

Prime Factorization of 821

Before finding the factors of 821 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 821, 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 821 can be expressed as:

821 = 1 x 821

Factors of 821 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.

Factors of 821 in Pairs

For 821, the factor pairs can be found as:

1 x 821 = 821

The possible factor pairs of 821 are given as (1, 821).

All these numbers in pairs, when multiplied, give 821 as the product.

The negative factor pairs of 821 are given as:

-1 x -821 = 821 

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 and -821 are called negative factors of 821.

The list of all the factors of 821, including positive as well as negative numbers, is given below.

Factor list of 812: 1, -1, 821, and -821

Factors of 821 Solved Examples

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

Example 1

How many factors of 821 are there?


The total number of Factors of 821 is 4.

Factors of 821 are 1 and 821.

Example 2

Find the factors of 821 using prime factorization.


The prime factorization of 821 is given as:

821 $\div$ 821 = 1 

So the prime factorization of 821 can be written as:

1 x 821 = 821

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