Factors of -27
2026-02-28 13:17 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-27

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Last updated on December 11, 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 -27, how they are used in real life, and the tips to learn them quickly.

What are the Factors of -27?

The numbers that divide -27 evenly are known as factors of -27.

A factor of -27 is a number that divides the number without remainder.

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

Negative factors of -27: -1, -3, -9, and -27.

Prime factors of -27: 3.

Prime factorization of -27: -1 × 3³.

The sum of factors of -27: 1 + 3 + 9 + 27 = 40.

How to Find Factors of -27?

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 the pairs of numbers that are multiplied to give -27. Identifying the numbers which are multiplied to get the number -27 is the multiplication method.

Step 1: Multiply -27 by -1, -27 × -1 = 27.

Step 2: Check for other numbers that give -27 after multiplying

-1 × 27 = -27

-3 × 9 = -27

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

For every positive factor, there is a corresponding 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 the simple division method

Step 1: Divide -27 by -1, -27 ÷ -1 = 27.

Step 2: Continue dividing -27 by the numbers until the remainder becomes 0.

-27 ÷ -1 = 27

-27 ÷ -3 = 9

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

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 -27 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

-27 ÷ -3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of -27 are 3.

The prime factorization of -27 is: -1 × 3³.

Factor Tree

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

Step 1: Firstly, -27 is divided by -3 to get 9.

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

Step 3: Then divide 3 by 3 to get 1. Here, 3 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of -27 is: -1 × 3³.

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

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

Common Mistakes and How to Avoid Them in Factors of -27

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 3 shelves and -27 books to arrange. How will they divide it equally?

Okay, lets begin

Each shelf will have -9 books.

Explanation

To divide the books equally, we need to divide the total books by the number of shelves.

-27/3 = -9

Well explained 👍

Problem 2

A baker has -27 cupcakes to place in boxes, and each box can hold 9 cupcakes. How many boxes does the baker need?

Okay, lets begin

The baker needs -3 boxes.

Explanation

To find out how many boxes are needed, divide the total number of cupcakes by the number each box can hold.

-27/9 = -3

Well explained 👍

Problem 3

A group of people want to split -27 apples into bags with 3 apples each. How many bags do they need?

Okay, lets begin

They need -9 bags.

Explanation

To find the number of bags, divide the total apples by the number of apples per bag.

-27/3 = -9

Well explained 👍

Problem 4

A company is distributing -27 pens equally among 9 departments. How many pens will each department receive?

Okay, lets begin

Each department will receive -3 pens.

Explanation

To find the number of pens each department will receive, divide the total pens by the number of departments. -27/9 = -3

Well explained 👍

Problem 5

A gardener has -27 plants and wants to create rows of 3 plants each. How many rows can he create?

Okay, lets begin

He can create -9 rows.

Explanation

Divide the total number of plants by the number of plants per row.

-27/3 = -9

Well explained 👍

FAQs on Factors of -27

1.What are the factors of -27?

1, 3, 9, 27 are the factors of -27.

2.Mention the prime factors of -27.

The prime factor of -27 is 3.

3.Is -27 a multiple of 3?

4.Mention the factor pairs of -27?

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

5.What is the cube of 3?

Important Glossaries for Factor of -27

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -27 are 1, 3, 9, and 27.
     
  • Prime factors: The factors which are prime numbers. For example, 3 is a prime factor of -27.
     
  • 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 -27 are (1, 27), (3, 9).
     
  • Negative factors: Factors that are negative numbers. For example, -1, -3, -9, and -27 are the negative factors of -27.
     
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of -27 is -1 × 3³.

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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.