Factors of -90
2026-02-28 08:43 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-90

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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 -90, how they are used in real life, and tips to learn them quickly.

What are the Factors of -90?

The numbers that divide -90 evenly are known as factors of -90.

A factor of -90 is a number that divides the number without a remainder.

The factors of -90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Negative factors of -90: -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90.

Prime factors of -90: 2, 3, and 5.

Prime factorization of -90: -1 × 2 × 3² × 5.

The sum of the positive factors of 90: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234.

How to Find Factors of -90?

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 -90. Identifying the numbers which are multiplied to get the number -90 is the multiplication method.

Step 1: Multiply -90 by 1, -90 × 1 = -90.

Step 2: Check for other numbers that give -90 after multiplying

2 × -45 = -90

-2 × 45 = -90

3 × -30 = -90

-3 × 30 = -90

5 × -18 = -90

-5 × 18 = -90

6 × -15 = -90

-6 × 15 = -90

9 × -10 = -90

-9 × 10 = -90

Therefore, the positive factor pairs of -90 are: (1, -90), (2, -45), (3, -30), (5, -18), (6, -15), and (9, -10).

For every positive factor, there is a corresponding negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with 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 -90 by 1, -90 ÷ 1 = -90.

Step 2: Continue dividing -90 by the numbers until the remainder becomes 0.

-90 ÷ 1 = -90

-90 ÷ 2 = -45

-90 ÷ 3 = -30

-90 ÷ 5 = -18

-90 ÷ 6 = -15

-90 ÷ 9 = -10

Therefore, the factors of -90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

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 -90 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

-90 ÷ -1 = 90

90 ÷ 2 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

The prime factors of -90 are -1, 2, 3, and 5.

The prime factorization of -90 is: -1 × 2 × 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, 90 is divided by 2 to get 45.

Step 2: Now divide 45 by 3 to get 15.

Step 3: Then divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of -90 is: -1 × 2 × 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 -90: (1, -90), (2, -45), (3, -30), (5, -18), (6, -15), and (9, -10).

Negative factor pairs of -90: (-1, 90), (-2, 45), (-3, 30), (-5, 18), (-6, 15), and (-9, 10).

Common Mistakes and How to Avoid Them in Factors of -90

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 -90 points to distribute. How will they distribute it equally?

Okay, lets begin

They will distribute -10 points to each team.

Explanation

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

-90/9 = -10

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 15 meters and the total area is -90 square meters. Find the width?

Okay, lets begin

-6 meters.

Explanation

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

Area = length × width

-90 = 15 × width

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

-90/15 = width

Width = -6.

Well explained 👍

Problem 3

There are 5 boxes and -90 marbles. How many marbles will be in each box?

Okay, lets begin

Each box will have -18 marbles.

Explanation

To find the marbles in each box, divide the total marbles by the boxes.

-90/5 = -18

Well explained 👍

Problem 4

In a class, there are -90 points to distribute, and 10 groups. How many points are distributed to each group?

Okay, lets begin

Each group gets -9 points.

Explanation

Dividing the points by the total groups, we will get the number of points each group gets.

-90/10 = -9

Well explained 👍

Problem 5

There are -90 plants to distribute in 6 gardens. How many plants will go in each garden?

Okay, lets begin

Each garden will receive -15 plants.

Explanation

Divide the total plants by the gardens.

-90/6 = -15

Well explained 👍

FAQs on Factors of -90

1.What are the factors of -90?

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90 are the factors of -90.

2.Mention the prime factors of -90.

The prime factors of -90 are -1 × 2 × 3² × 5.

3.Is -90 a multiple of -5?

4.Mention the factor pairs of -90?

(1, -90), (2, -45), (3, -30), (5, -18), (6, -15), and (9, -10) are the factor pairs of -90.

5.What is the absolute value of -90?

Important Glossaries for Factors of -90

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of -90.
     
  • 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 -90 are (1, -90), (2, -45), etc.
     
  • Prime factorization: Expressing a number as the product of its prime factors. For example, -90 can be expressed as -1 × 2 × 3² × 5.
     
  • Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -90 is 90.

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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.