Factors of 821
2026-02-28 17:55 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 821, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 821?

The numbers that divide 821 evenly are known as factors of 821.

A factor of 821 is a number that divides the number without remainder.

The factors of 821 are 1, 7, 13, 91, 117, and 821.

Negative factors of 821: -1, -7, -13, -91, -117, and -821.

Prime factors of 821: 7 and 13.

Prime factorization of 821: 7 × 13².

The sum of factors of 821: 1 + 7 + 13 + 91 + 117 + 821 = 1050

How to Find Factors of 821?

Factors can be found using different methods. Mentioned below are some commonly used methods:

  • Finding factors using multiplication
     
  • Finding factors using division method
     
  • Prime factors and Prime factorization

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 821. Identifying the numbers which are multiplied to get the number 821 is the multiplication method.

Step 1: Multiply 821 by 1, 821 × 1 = 821.

Step 2: Check for other numbers that give 821 after multiplying

7 × 117 = 821

13 × 63 = 821

Therefore, the positive factor pairs of 821 are: (1, 821), (7, 117), and (13, 63).

All these factor pairs result in 821.

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method

Step 1: Divide 821 by 1, 821 ÷ 1 = 821.

Step 2: Continue dividing 821 by the numbers until the remainder becomes 0.

821 ÷ 1 = 821

821 ÷ 7 = 117

821 ÷ 13 = 63

Therefore, the factors of 821 are: 1, 7, 13, 91, 117, 821.

Prime Factors and Prime Factorization

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 821 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

821 ÷ 7 = 117

117 ÷ 13 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of 821 are 7 and 13.

The prime factorization of 821 is: 7 × 13².

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

Step 1: Firstly, 821 is divided by 7 to get 117.

Step 2: Now divide 117 by 13 to get 9.

Step 3: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 821 is: 7 × 13².

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 821: (1, 821), (7, 117), and (13, 63).

Negative factor pairs of 821: (-1, -821), (-7, -117), and (-13, -63).

Common Mistakes and How to Avoid Them in Factors of 821

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and ways to avoid them.

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Problem 1

There are 7 friends and 821 cards. How will they divide it equally?

Okay, lets begin

They will get 117 cards each.

Explanation

To divide the cards equally, we need to divide the total cards with the number of friends.

821/7 = 117

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 13 meters and the total area is 821 square meters. Find the width?

Okay, lets begin

63 meters.

Explanation

To find the width of the field, we use the formula, Area = length × width

821 = 13 × width

To find the value of width, we need to shift 13 to the left side.

821/13 = width

Width = 63.

Well explained 👍

Problem 3

There are 9 boxes and 821 marbles. How many marbles will be in each box?

Okay, lets begin

Each box will have 91 marbles.

Explanation

To find the marbles in each box, divide the total marbles with the boxes.

821/9 = 91

Well explained 👍

Problem 4

In a class, there are 821 students, and 13 groups. How many students are there in each group?

Okay, lets begin

There are 63 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

821/13 = 63

Well explained 👍

Problem 5

821 apples need to be arranged in 7 baskets. How many apples will go in each basket?

Okay, lets begin

Each basket has 117 apples.

Explanation

Divide total apples with baskets.

821/7 = 117

Well explained 👍

FAQs on Factors of 821

1.What are the factors of 821?

1, 7, 13, 91, 117, 821 are the factors of 821.

2.Mention the prime factors of 821.

The prime factors of 821 are 7 × 13².

3.Is 821 a multiple of 7?

4.Mention the factor pairs of 821?

(1, 821), (7, 117), and (13, 63) are the factor pairs of 821.

5.What is the square of 821?

Important Glossaries for Factors of 821

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 821 are 1, 7, 13, 91, 117, and 821.
  • Prime factors: The factors which are prime numbers. For example, 7 and 13 are prime factors of 821.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 821 are (1, 821), (7, 117), and (13, 63).
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 821 is 7 × 13².
  • Division method: A method to find factors by dividing the number by integers until the remainder is zero. For example, using the division method to find factors of 821 involves dividing it by 1, 7, and so on.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.