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Last updated on May 26th, 2025

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Factors of 827

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Factors are the numbers that divide any given number evenly without 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 827, how they are used in real life, and tips to learn them quickly.

Factors of 827 for US Students
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What are the Factors of 827?

The numbers that divide 827 evenly are known as factors of 827.

 

A factor of 827 is a number that divides the number without remainder.

 

The factors of 827 are 1 and 827.

 

Negative factors of 827: -1 and -827.

 

Since 827 is a prime number, it has no prime factors other than itself.

 

The prime factorization of 827 is simply 827.

 

The sum of factors of 827: 1 + 827 = 828

 

factors of 827

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How to Find Factors of 827?

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 827. For a prime number like 827, the only multiplication pair is:

 

Step 1: Multiply 827 by 1, 827 × 1 = 827.

 

Therefore, the only positive factor pair of 827 is: (1, 827).

 

For every positive factor, there is a corresponding negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with 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 the simple division method

 

Step 1: Divide 827 by 1, 827 ÷ 1 = 827.

 

Step 2: Continue dividing 827 by the numbers until the remainder becomes 0.

827 ÷ 1 = 827

 

Since 827 is a prime number, dividing by any number other than 1 and 827 results in a remainder.

 

Therefore, the factors of 827 are: 1 and 827.

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Prime Factors and Prime Factorization

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

 

  • Using prime factorization
     
  • Using a factor tree

 

Using Prime Factorization: In this process, prime factors of 827 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

 

Since 827 is a prime number, it cannot be broken down further.

 

The prime factorization of 827 is simply 827.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. In the case of 827, since it is a prime number, the factor tree is quite simple:

 

Step 1: 827 is a prime number and cannot be divided further. So, the prime factorization of 827 is simply 827.

 

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 827: (1, 827).

 

Negative factor pairs of 827: (-1, -827).

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Common Mistakes and How to Avoid Them in Factors of 827

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 the factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 827, 1 and 827 are factors.

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Factors of 827 Examples

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Problem 1

There are 2 teams and 827 apples. How will they divide it equally?

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They cannot divide the apples equally without a remainder.

Explanation

To divide the apples equally, we need to divide the total apples by the number of teams. Since 827 is a prime number, dividing by any number other than 1 or 827 will leave a remainder.

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Problem 2

A company has 827 chairs and wants to distribute them equally among 5 offices. How many chairs will each office receive?

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Each office will receive 165 chairs with 2 chairs remaining.

Explanation

To divide the chairs equally, we divide the total number of chairs by the number of offices.

827 ÷ 5 = 165 R2

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Problem 3

There are 827 students and 3 buses. How many students will be on each bus?

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Each bus will have 275 students with 2 students remaining.

Explanation

To find the number of students on each bus, divide the total students by the number of buses.

827 ÷ 3 = 275 R2

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Problem 4

An estate agent has 827 houses and wants to allocate them equally among 7 managers. How many houses will each manager get?

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Each manager will get 118 houses with 1 house remaining.

Explanation

To allocate the houses equally, we divide the total number of houses by the number of managers.

827 ÷ 7 = 118 R1

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Problem 5

A library has 827 books that need to be distributed evenly across 4 sections. How many books will each section have?

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Each section will have 206 books with 3 books remaining.

Explanation

Divide the total books by the number of sections.

827 ÷ 4 = 206 R3

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FAQs on Factors of 827

1.What are the factors of 827?

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2.Is 827 a prime number?

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3.Is 827 a multiple of 3?

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4.Mention the factor pairs of 827?

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5.What is the square of 827?

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6.How can children in United States use numbers in everyday life to understand Factors of 827?

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7.What are some fun ways kids in United States can practice Factors of 827 with numbers?

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8.What role do numbers and Factors of 827 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 827 skills?

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Important Glossaries for Factors of 827

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 827 are 1 and 827.

 

  • Prime factors: The factors which are prime numbers. For example, 827 itself is a prime factor since 827 is a prime number.

 

  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 827 is (1, 827).

 

  • Prime number: A number that has only two distinct factors: 1 and itself. For example, 827 is a prime number.

 

  • Remainder: The amount left over after division when a number cannot be evenly divided. For example, dividing 827 by any number other than 1 or 827 results in a remainder.
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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 827, 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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