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Last updated on May 26th, 2025

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Factors of 820

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Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 820, how they are used in real life, and tips to learn them quickly.

Factors of 820 for US Students
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What are the Factors of 820?

The numbers that divide 820 evenly are known as factors of 820.

 

A factor of 820 is a number that divides the number without a remainder.

 

The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820.

 

Negative factors of 820: -1, -2, -4, -5, -10, -20, -41, -82, -164, -205, -410, and -820.

 

Prime factors of 820: 2, 5, and 41.

 

Prime factorization of 820: (22 times 5 times 41).

 

The sum of factors of 820: 1 + 2 + 4 + 5 + 10 + 20 + 41 + 82 + 164 + 205 + 410 + 820 = 1764

 

factors of 820

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How to Find Factors of 820?

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
     
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 820. Identifying the numbers which are multiplied to get the number 820 is the multiplication method.

 

Step 1: Multiply 820 by 1, 820 × 1 = 820.

 

Step 2: Check for other numbers that give 820 after multiplying

2 × 410 = 820     

4 × 205 = 820     

5 × 164 = 820     

10 × 82 = 820     

20 × 41 = 820

 

Therefore, the positive factor pairs of 820 are: (1, 820), (2, 410), (4, 205), (5, 164), (10, 82), (20, 41). 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 820 by 1, 820 ÷ 1 = 820.

 

Step 2: Continue dividing 820 by the numbers until the remainder becomes 0.

820 ÷ 1 = 820

820 ÷ 2 = 410

820 ÷ 4 = 205

820 ÷ 5 = 164

820 ÷ 10 = 82

820 ÷ 20 = 41

 

Therefore, the factors of 820 are: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820.

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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
     
  • Using factor tree

 

Using Prime Factorization: In this process, prime factors of 820 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

820 ÷ 2 = 410

410 ÷ 2 = 205

205 ÷ 5 = 41

41 ÷ 41 = 1

 

The prime factors of 820 are 2, 5, and 41.

 

The prime factorization of 820 is: (22 times 5 times 41).

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Factor Tree

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

 

Step 1: Firstly, 820 is divided by 2 to get 410.

 

Step 2: Now divide 410 by 2 to get 205.

 

Step 3: Then divide 205 by 5 to get 41. Here, 41 is a prime number, which cannot be divided anymore. So, the prime factorization of 820 is: (22 times 5 times 41).

 

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 820: (1, 820), (2, 410), (4, 205), (5, 164), (10, 82), and (20, 41).

 

Negative factor pairs of 820: (-1, -820), (-2, -410), (-4, -205), (-5, -164), (-10, -82), and (-20, -41).

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Common Mistakes and How to Avoid Them in Factors of 820

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

Mistake 1

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Forgetting the number itself and 1 is a factor

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Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 820, 1 and 820 are also factors.

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Factors of 820 Examples

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Problem 1

There are 41 students and 820 pencils. How will they distribute them equally?

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Each student will get 20 pencils.

Explanation

To distribute the pencils equally, we need to divide the total pencils by the number of students.

820/41 = 20

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Problem 2

An auditorium has 205 chairs arranged in rows. The total capacity is 820 people. How many rows are there?

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4 rows.

Explanation

To find the number of rows, use the formula, Capacity = rows × chairs per row

820 = rows × 205

To find the number of rows, divide the total capacity by chairs per row.

820/205 = 4

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Problem 3

There are 10 teams and 820 points available. How many points will each team get if divided equally?

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Each team will get 82 points.

Explanation

To find the points each team will receive, divide the total points by the number of teams.

820/10 = 82

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Problem 4

A company has 820 tasks to complete and 5 departments. How many tasks will each department have?

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Each department will have 164 tasks.

Explanation

Dividing the tasks by the total departments, we will get the number of tasks per department.

820/5 = 164

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Problem 5

820 books need to be placed in 2 libraries. How many books will each library receive?

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Each library will have 410 books.

Explanation

Divide the total books by the number of libraries.

820/2 = 410

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FAQs on Factors of 820

1.What are the factors of 820?

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2.Mention the prime factors of 820.

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3.Is 820 a multiple of 4?

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4.Mention the factor pairs of 820?

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5.What is the square of 820?

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6.How can children in United States use numbers in everyday life to understand Factors of 820?

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7.What are some fun ways kids in United States can practice Factors of 820 with numbers?

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8.What role do numbers and Factors of 820 play in helping children in United States develop problem-solving skills?

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9.How can families in United States create number-rich environments to improve Factors of 820 skills?

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Important Glossaries for Factor of 820

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 5, and 41 are prime factors of 820.

 

  • 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 820 are (1, 820), (2, 410), etc.

 

  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 820 is (22 times 5 times 41).

 

  • Negative factors: The negative counterparts of the positive factors. For example, -1, -2, -4, etc., are negative factors of 820.
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About BrightChamps in United States

At BrightChamps, we believe numbers are more than symbols—they unlock a world full of possibilities! Our goal is to support kids throughout the United States in mastering key math skills, such as today’s Factors of 820, with a special emphasis on understanding factors—in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, tracking scores at a Little League baseball game, or budgeting their allowance to buy cool gadgets, understanding numbers builds their confidence for everyday tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA learn in unique ways, we customize our methods to match each child’s style. From the busy streets of New York City to the sunny beaches of California, BrightChamps makes math come alive, bringing it closer to children everywhere. Let’s turn factors into an exciting part of every child’s math adventure!
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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.

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Fun Fact

: She loves to read number jokes and games.

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