Factors of -180
2026-02-28 11:21 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-180

306 Learners

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 -180, how they are used in real life, and tips to learn them quickly.

What are the Factors of -180?

The numbers that divide -180 evenly are known as factors of -180.

A factor of -180 is a number that divides the number without a remainder.

The positive factors of -180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

Negative factors of -180: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, and -180.

Prime factors of 180: 2, 3, and 5.

Prime factorization of 180: 2² × 3² × 5.

The sum of the positive factors of 180: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180 = 546

How to Find Factors of -180?

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 180. Identifying the numbers which are multiplied to get the number 180 is the multiplication method.

Step 1: Multiply 180 by 1, 180 × 1 = 180.

Step 2: Check for other numbers that give 180 after multiplying

2 × 90 = 180

3 × 60 = 180

4 × 45 = 180

5 × 36 = 180

6 × 30 = 180

9 × 20 = 180

10 × 18 = 180

12 × 15 = 180

Therefore, the positive factor pairs of 180 are: (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18), (12, 15).

For every positive factor, there is a negative factor.

Explore Our Programs

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 180 by 1, 180 ÷ 1 = 180.

Step 2: Continue dividing 180 by the numbers until the remainder becomes 0.

180 ÷ 1 = 180

180 ÷ 2 = 90

180 ÷ 3 = 60

180 ÷ 4 = 45

180 ÷ 5 = 36

180 ÷ 6 = 30

180 ÷ 9 = 20

180 ÷ 10 = 18

180 ÷ 12 = 15

Therefore, the factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

Prime Factors and Prime Factorization

The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 180 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

180 ÷ 2 = 90

90 ÷ 2 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

The prime factors of 180 are 2, 3, and 5.

The prime factorization of 180 is: 2² × 3² × 5.

Factor Tree

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

Step 1: Firstly, 180 is divided by 2 to get 90.

Step 2: Now divide 90 by 2 to get 45.

Step 3: Then divide 45 by 3 to get 15.

Step 4: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 180 is: 2² × 3² × 5.

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 180: (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18), (12, 15).

Negative factor pairs of -180: (-1, -180), (-2, -90), (-3, -60), (-4, -45), (-5, -36), (-6, -30), (-9, -20), (-10, -18), (-12, -15).

Common Mistakes and How to Avoid Them in Factors of -180

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 36 apples and -180 oranges. How will they divide the oranges equally?

Okay, lets begin

Each will get 5 oranges.

Explanation

To divide the oranges equally, we need to divide the total oranges with the number of apples.

-180/36 = 5

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden is 15 meters and the total area is -180 square meters. Find the width?

Okay, lets begin

-12 meters.

Explanation

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

Area = length × width

-180 = 15 × width

To find the value of width, we need to shift 15 to the left side.

-180/15 = width

Width = -12.

Well explained 👍

Problem 3

There are 45 boxes and -180 candies. How many candies will be in each box?

Okay, lets begin

Each box will have 4 candies.

Explanation

To find the candies in each box, divide the total candies with the boxes.

-180/45 = 4

Well explained 👍

Problem 4

In a class, there are -180 students, and 9 groups. How many students are there in each group?

Okay, lets begin

There are -20 students in each group.

Explanation

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

-180/9 = -20

Well explained 👍

Problem 5

-180 books need to be arranged in 15 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has -12 books.

Explanation

Divide total books with shelves.

-180/15 = -12

Well explained 👍

FAQs on Factors of -180

1.What are the factors of -180?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are the factors of 180. The negative factors of -180 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, -180.

2.Mention the prime factors of -180.

The prime factors of 180 are 2² × 3² × 5.

3.Is -180 a multiple of 9?

4.Mention the factor pairs of -180?

(1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18), (12, 15) are the positive factor pairs of 180. The negative factor pairs of -180 are (-1, -180), (-2, -90), (-3, -60), (-4, -45), (-5, -36), (-6, -30), (-9, -20), (-10, -18), (-12, -15).

5.What is the square of 180?

Important Glossaries for Factor of -180

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180 along with their negative counterparts.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 180.
     
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the positive factor pairs of 180 are (1, 180), (2, 90), etc.
     
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 180 is 2² × 3² × 5.
     
  • Negative factors: Factors that are negative counterparts of positive factors. For example, the negative factors of -180 include -1, -2, -3, etc.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.