Factors of -87
2026-02-28 09:58 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-87

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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without 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 -87, how they are used in real life, and tips to learn them quickly.

What are the Factors of -87?

The numbers that divide -87 evenly are known as factors of -87.

A factor of -87 is a number that divides the number without remainder.

The Posituve factors of -87 are 1, 3, 29, and 87.

Negative factors of -87: -1, -3, -29, and -87.

Prime factors of -87: 3 and 29.

Prime factorization of -87: -1 × 3 × 29.

The sum of positive factors of 87: 1 + 3 + 29 + 87 = 120

How to Find Factors of -87?

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 -87. Identifying the numbers which are multiplied to get the number -87 is the multiplication method.

Step 1: Multiply -87 by 1, -87 × 1 = -87.

Step 2: Check for other numbers that give -87 after multiplying 3 × -29 = -87

Therefore, the positive factor pairs of -87 are: (1, 87), (3, 29).

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 a simple division method 

Step 1: Divide -87 by 1, -87 ÷ 1 = -87.

Step 2: Continue dividing -87 by the numbers until the remainder becomes 0.

-87 ÷ 1 = -87

-87 ÷ 3 = -29

Therefore, the factors of -87 are: 1, 3, 29, 87.

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 -87 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

-87 ÷ 3 = -29

-29 ÷ 29 = -1

The prime factors of -87 are 3 and 29.

The prime factorization of -87 is: -1 × 3 × 29.

Factor Tree

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

Step 1: Firstly, -87 is divided by 3 to get -29. Here, -29 is a negative prime number.

So, the prime factorization of -87 is: -1 × 3 × 29.

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 -87: (1, 87), (3, 29).

Negative factor pairs of -87: (-1, -87), (-3, -29).

Common Mistakes and How to Avoid Them in Factors of -87

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

A company has -87 units of loss. If they divide the loss equally among 3 departments, how much loss will each department bear?

Okay, lets begin

Each department will bear -29 units of loss.

Explanation

To divide the loss equally, we need to divide the total loss by the number of departments.

-87/3 = -29

Well explained 👍

Problem 2

A rectangle has a total area of -87 square meters, and the width is 3 meters. Find the length?

Okay, lets begin

-29 meters.

Explanation

To find the length of the rectangle, we use the formula, Area = length × width -87 = length × 3

To find the value of length, we need to shift 3 to the left side.

-87/3 = length

Length = -29.

Well explained 👍

Problem 3

A refrigerator is set to -87 degrees and has three cooling sections. If each section has an equal drop in temperature, what is the temperature drop in each section?

Okay, lets begin

Each section experiences -29 degrees of temperature drop.

Explanation

To find the temperature drop in each section, divide the total temperature by the sections.

-87/3 = -29

Well explained 👍

Problem 4

There are 87 students in a class, and they are divided into 3 teams. How many students are in each team?

Okay, lets begin

There are 29 students in each team.

Explanation

Dividing the students with the total teams, we will get the number of students in each team.

87/3 = 29

Well explained 👍

Problem 5

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

Okay, lets begin

Each of the shelves has 29 books.

Explanation

Divide total books by shelves.

87/3 = 29

Well explained 👍

FAQs on Factors of -87

1.What are the factors of -87?

1, 3, 29, and 87 are the factors of -87.

2.Mention the prime factors of -87.

The prime factors of -87 are 3 and 29.

3.Is 87 a multiple of 3?

4.Mention the factor pairs of -87?

(1, 87), (3, 29) are the positive factor pairs of -87.

5.What is the product of the prime factors of -87?

The product of the prime factors of -87 is -1 × 3 × 29 = -87.

Important Glossaries for Factors of -87

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -87 are 1, 3, 29, and 87.
  • Prime factors: The factors which are prime numbers. For example, 3 and 29 are prime factors of -87.
  • 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 -87 are (1, 87), (3, 29).
  • Negative factors: These are factors of a number that are negative. For example, -1, -3, -29, and -87 for -87.
  • Prime factorization: This is the expression of a number as the product of its prime factors. For example, the prime factorization of -87 is -1 × 3 × 29.

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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.