Factors of -36
2026-02-28 06:21 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus--36

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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 -36, how they are used in real life, and tips to learn them quickly.

What are the Factors of -36?

The numbers that divide -36 evenly are known as factors of -36.

A factor of -36 is a number that divides the number without a remainder.

The factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Negative factors of -36: -1, -2, -3, -4, -6, -9, -12, -18, and -36.

Prime factors of -36: 2 and 3.

Prime factorization of -36: 2² × 3².

The sum of factors of 36 (ignoring the negative sign): 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91

How to Find Factors of -36?

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

  • Finding factors using multiplication
     
  • Finding factors using the 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 -36. Identifying the numbers which are multiplied to get the number -36 is the multiplication method.

Step 1: Multiply -36 by 1, -36 × 1 = -36.

Step 2: Check for other numbers that give -36 after multiplying -1 × 36 = -36

-2 × 18 = -36

-3 × 12 = -36

-4 × 9 = -36

-6 × 6 = -36

Therefore, the positive factor pairs of -36 are: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6).

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 as whole numbers as factors. Factors can be calculated by following the simple division method 

Step 1: Divide -36 by 1, -36 ÷ 1 = -36.

Step 2: Continue dividing -36 by the numbers until the remainder becomes 0.

-36 ÷ 1 = -36

-36 ÷ 2 = -18

-36 ÷ 3 = -12

-36 ÷ 4 = -9

-36 ÷ 6 = -6

Therefore, the factors of -36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.

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 -36 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of -36 are 2 and 3.

The prime factorization of -36 is: 2² × 3².

Factor Tree

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

Step 1: Firstly, 36 is divided by 2 to get 18.

Step 2: Now divide 18 by 2 to get 9.

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

Step 4: Divide 3 by 3 to get 1. Here, 3 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of -36 is: 2² × 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 -36: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).

Negative factor pairs of -36: (-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).

Common Mistakes and How to Avoid Them in Factors of -36

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 teams and -36 points to distribute. How will they divide it equally?

Okay, lets begin

They will get -4 points each.

Explanation

To divide the points equally, we need to divide the total points by the number of teams.

-36/9 = -4

Well explained 👍

Problem 2

A rectangular garden has a length of 6 meters and a total area of -36 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

-36 = 6 × width

To find the value of width, we need to shift 6 to the left side.

-36/6 = width

Width = -6.

Well explained 👍

Problem 3

There are 12 baskets and -36 apples. 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 number of baskets.

-36/12 = -3

Well explained 👍

Problem 4

In a school, there are -36 students, and 3 groups. How many students are there in each group?

Okay, lets begin

There are -12 students in each group.

Explanation

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

-36/3 = -12

Well explained 👍

Problem 5

-36 books need to be arranged in 9 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has -4 books.

Explanation

Divide total books by shelves.

-36/9 = -4

Well explained 👍

FAQs on Factors of -36

1.What are the factors of -36?

1, 2, 3, 4, 6, 9, 12, 18, 36 are the factors of -36.

2.Mention the prime factors of -36.

The prime factors of -36 are 2² × 3².

3.Is -36 a multiple of 3?

4.Mention the factor pairs of -36?

(1, 36), (2, 18), (3, 12), (4, 9), and (6, 6) are the factor pairs of -36.

5.What is the square of -36?

Important Glossaries for Factor of -36

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
  • Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of -36.
  • 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 -36 are (1, 36), (2, 18), etc.
  • Negative factors: Factors that are negative. For example, -1, -2, -3, etc., are negative factors of -36.
  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of -36 is 2² × 3².

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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.