Factors of 831
2026-02-28 13:42 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 831, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 831?

The numbers that divide 831 evenly are known as factors of 831. A factor of 831 is a number that divides the number without remainder. The factors of 831 are 1, 3, 277, and 831.

Negative factors of 831: -1, -3, -277, and -831.

Prime factors of 831: 3 and 277.

Prime factorization of 831: 3 × 277.

The sum of factors of 831: 1 + 3 + 277 + 831 = 1112

How to Find Factors of 831?

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 831. Identifying the numbers which are multiplied to get the number 831 is the multiplication method.

Step 1: Multiply 831 by 1, 831 × 1 = 831.

Step 2: Check for other numbers that give 831 after multiplying   

3 × 277 = 831

Therefore, the positive factor pairs of 831 are: (1, 831) and (3, 277). All these factor pairs result in 831. 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 in whole numbers as factors. Factors can be calculated by following the simple division method -

Step 1: Divide 831 by 1, 831 ÷ 1 = 831.

Step 2: Continue dividing 831 by the numbers until the remainder becomes 0.

831 ÷ 1 = 831

831 ÷ 3 = 277

Therefore, the factors of 831 are: 1, 3, 277, 831.

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 831 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

831 ÷ 3 = 277

277 ÷ 277 = 1

The prime factors of 831 are 3 and 277. The prime factorization of 831 is: 3 × 277.

Factor Tree

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

Step 1: Firstly, 831 is divided by 3 to get 277.

Step 2: Now divide 277 by 277 to get 1. So, the prime factorization of 831 is: 3 × 277.

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 831: (1, 831) and (3, 277).
  • Negative factor pairs of 831: (-1, -831) and (-3, -277).

Common Mistakes and How to Avoid Them in Factors of 831

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

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Problem 1

There are 3 friends and 831 marbles. How will they divide it equally?

Okay, lets begin

They will get 277 marbles each.

Explanation

To divide the marbles equally, we need to divide the total marbles by the number of friends.

831/3 = 277

Well explained 👍

Problem 2

A rectangular garden has a width of 3 meters and the total area is 831 square meters. Find the length.

Okay, lets begin

The length is 277 meters.

Explanation

To find the length of the garden, we use the formula,     

Area = length × width     

831 = length × 3     

To find the value of length, we need to shift 3 to the left side.    

 831/3 = length    

Length = 277.

Well explained 👍

Problem 3

There are 831 apples and 277 baskets. How many apples will be in each basket?

Okay, lets begin

Each basket will have 3 apples.

Explanation

To find the apples in each basket, divide the total apples by the baskets.     

831/277 = 3

Well explained 👍

Problem 4

In a class, there are 831 students, and 3 buses. How many students are there in each bus?

Okay, lets begin

There are 277 students in each bus.

Explanation

Dividing the students by the total buses, we will get the number of students in each bus.     

831/3 = 277

Well explained 👍

Problem 5

831 books need to be arranged in 277 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 3 books.

Explanation

Divide total books by shelves.    

831/277 = 3

Well explained 👍

FAQs on Factors of 831

1.What are the factors of 831?

1, 3, 277, 831 are the factors of 831.

2.Mention the prime factors of 831.

The prime factors of 831 are 3 × 277.

3.Is 831 a multiple of 3?

4.Mention the factor pairs of 831?

(1, 831) and (3, 277) are the factor pairs of 831.

5.What is the square of 831?

Important Glossaries for Factors of 831

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 831 are 1, 3, 277, and 831.
  • Prime factors: The factors which are prime numbers. For example, 3 and 277 are prime factors of 831.
  • 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 831 are (1, 831) and (3, 277).
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 831 is 3 × 277.
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number, such as finding that 3 × 277 equals 831.

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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.