Factors of -81
2026-02-28 19:10 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-81

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Last updated on December 12, 2025

Factors are numbers that divide a 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 -81, how they are used in real life, and tips to learn them quickly.

What are the Factors of -81?

The numbers that divide -81 evenly are known as factors of -81.

A factor of -81 is a number that divides the number without leaving a remainder.

The Positive factors of -81 are 1, 3, 9, 27, 81,

The negative factors of -81: -1, -3, -9, -27, -81.

Prime factors of -81: 3.

Prime factorization of -81: 34.

The sum of factors of 81 (ignoring the negative factors): 1 + 3 + 9 + 27 + 81 = 121.

How to Find Factors of -81?

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

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify pairs of numbers that multiply to give -81. Identifying the numbers which are multiplied to get -81 is the multiplication method.

Step 1: Multiply -81 by 1, -81 × 1 = -81.

Step 2: Check for other numbers that give -81when multiplied:

3 × -27 = -81

9 × -9 = -81

27 × -3 = -81

81 × -1 = -81

Therefore, the factor pairs of -81 are: (1, -81), (3, -27), (9, -9), (-1, 81), (-3, 27), (-9, 9).

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Divide the given number by whole numbers until the remainder becomes zero, and list out the numbers which result in whole numbers as factors. Factors can be calculated using the division method:

Step 1: Divide -81 by -1, -81 ÷ -1 = 81.

Step 2: Continue dividing -81 by numbers until the remainder becomes 0.

-81 ÷ 1 = -81

-81 ÷ 3 = -27

-81 ÷ 9 = -9

-81 ÷ 27 = -3

-81 ÷ 81 = -1

Therefore, the factors of -81 are: 1, 3, 9, 27, 81, -1, -3, -9, -27, -81.

Prime Factors and Prime Factorization

Factors can be found by dividing the number by prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of -81 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factorization of 81 is: 3^4. Thus, the prime factors of -81 are 3.

Factor Tree

The factor tree is a graphical representation of breaking down a number into prime factors. The following steps show:

Step 1: Firstly, divide 81 by 3 to get 27.

Step 2: Now divide 27 by 3 to get 9.

Step 3: Then divide 9 by 3 to get 3.

Step 4: Divide 3 by 3 to get 1.

So, the prime factorization of -81 is: 3^4.

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 -81: (1, -81), (3, -27), (9, -9).

Negative factor pairs of -81: (-1, 81), (-3, 27), (-9, 9).

Common Mistakes and How to Avoid Them in Factors of -81

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

Problem 1

There are 9 players and -81 points to distribute. How will they divide the points equally?

Okay, lets begin

They will get -9 points each.

Explanation

To divide the points equally, divide the total points by the number of players.

-81/9 = -9

Well explained 👍

Problem 2

A garden is rectangular, with the length of the garden being 27 meters and the total area being -81 square meters. Find the width.

Okay, lets begin

-3 meters.

Explanation

To find the width of the garden, use the formula: Area = length × width -81 = 27 × width

To find the value of width, shift 27 to the left side.

-81/27 = width

Width = -3.

Well explained 👍

Problem 3

A warehouse has 27 crates and -81 items. How many items will be in each crate?

Okay, lets begin

Each crate will have -3 items.

Explanation

To find the items in each crate, divide the total items by the crates.

-81/27 = -3

Well explained 👍

Problem 4

In a school, there are -81 students and 3 groups. How many students are there in each group?

Okay, lets begin

There are -27 students in each group.

Explanation

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

-81/3 = -27

Well explained 👍

Problem 5

81 books need to be arranged on 9 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 9 books.

Explanation

Divide the total books by the number of shelves.

81/9 = 9

Well explained 👍

FAQs on Factors of -81

1.What are the factors of -81?

The factors of -81 are 1, 3, 9, 27, 81, -1, -3, -9, -27, -81.

2.Mention the prime factors of -81.

The prime factors of -81 are 3.

3.Is -81 a multiple of 9?

4.Mention the factor pairs of -81.

(1, -81), (3, -27), (9, -9), (-1, 81), (-3, 27), (-9, 9) are the factor pairs of -81.

5.What is the square of -81?

Important Glossaries for Factors of -81

  • Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -81 are 1, 3, 9, 27, 81, and their negative counterparts.
  • Prime factors: Factors that are prime numbers. For example, 3 is a prime factor of -81.
  • Factor pairs: Two numbers in a pair that multiply to give the original number are called factor pairs. For example, the factor pairs of -81 are (1, -81), (3, -27), etc.
  • Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of -81 is 34.
  • Negative factors: Factors of a number that are negative. For example, the negative factors of -81 are -1, -3, -9, -27, -81.

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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.