Factors of -18
2026-02-28 11:36 Diff
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Last updated on December 11, 2025

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 -18, how they are used in real life, and tips to learn them quickly.

What are the Factors of -18?

The numbers that divide -18 evenly are known as factors of -18.

A factor of -18 is a number that divides the number without remainder.

The positive factors of -18 are 1, 2, 3, 6, 9, and 18.


The negative factors of -18:  -1, -2, -3, -6, -9, and -18.


Prime factors of -18: 2 and 3.


Prime factorization of -18: -1 × 2 × 3².
 

The sum of the positive factors of 18: 1 + 2 + 3 + 6 + 9 + 18 = 39

How to Find Factors of -18?

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 -18. Identifying the numbers which are multiplied to get the number -18 is the multiplication method.

Step 1: Multiply -18 by -1, -18 × -1 = 18.

Step 2: Check for other numbers that give 18 after multiplying

1 × 18 = 18

2 × 9 = 18

3 × 6 = 18

Therefore, the positive factor pairs of 18 are: (1, 18), (2, 9), (3, 6).

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given number by 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 a simple division method

Step 1: Divide -18 by -1, -18 ÷ -1 = 18.

Step 2: Continue dividing -18 by the numbers until the remainder becomes 0.

18 ÷ 1 = 18

18 ÷ 2 = 9

18 ÷ 3 = 6

Therefore, the factors of -18 are: 1, 2, 3, 6, 9, 18, -1, -2, -3, -6, -9, -18.

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 -18 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of -18 are 2 and 3.

The prime factorization of -18 is: -1 × 2 × 3².

Factor Tree

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

Step 1: Firstly, 18 is divided by 2 to get 9.

Step 2: Now divide 9 by 3 to get 3. 

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

So, the prime factorization of -18 is: -1 × 2 × 3².

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 18: (1, 18), (2, 9), (3, 6).

Negative factor pairs of -18: (-1, -18), (-2, -9), (-3, -6).

Common Mistakes and How to Avoid Them in Factors of -18

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 18 apples and 9 baskets. How will they divide them equally?

Okay, lets begin

They will get 2 apples in each basket.

Explanation

To divide the apples equally, we need to divide the total apples by the number of baskets.
18/9 = 2

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden is 3 meters and the total area is 18 square meters. Find the width?

Okay, lets begin

6 meters.

Explanation

To find the width of the garden, we use the formula,
Area = length × width
18 = 3 × width
To find the value of the width, we need to shift 3 to the left side.
18/3 = width
 

Width = 6.

Well explained 👍

Problem 3

There are 6 boxes and 18 chocolates. How many chocolates will be in each box?

Okay, lets begin

Each box will have 3 chocolates.

Explanation

To find the chocolates in each box, divide the total chocolates by the boxes.
18/6 = 3

Well explained 👍

Problem 4

In a class, there are 18 students, and 2 groups. How many students are there in each group?

Okay, lets begin

There are 9 students in each group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.
18/2 = 9

Well explained 👍

Problem 5

18 books need to be arranged in 3 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 6 books.

Explanation

Divide total books by shelves.
18/3 = 6

Well explained 👍

FAQs on Factors of -18

1.What are the factors of -18?

1, 2, 3, 6, 9, 18, -1, -2, -3, -6, -9, -18 are the factors of -18.

2.Mention the prime factors of -18.

The prime factors of -18 are 2 and 3.

3.Is -18 a multiple of 3?

4.Mention the factor pairs of -18?

(1, 18), (2, 9), (3, 6) and (-1, -18), (-2, -9), (-3, -6) are the factor pairs of -18.

5.What is the square of -18?

Important Glossaries for Factors of -18

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -18 are 1, 2, 3, 6, 9, 18, -1, -2, -3, -6, -9, and -18.
     
  • Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of -18.
     
  • 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 18 are (1, 18), (2, 9), etc.
     
  • Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the target number.
     
  • Division method: A technique to find factors by dividing the target number by whole numbers to see which result in a whole number quotient.

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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.