Factors of 90
2026-02-21 20:28 Diff
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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 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 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: 2 × 3² × 5. The sum of 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 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 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 3 × 30 = 90 5 × 18 = 90 6 × 15 = 90 9 × 10 = 90 Therefore, the positive factor pairs of 90 are: (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), (9, 10). For every positive factor, there is a 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 as 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, 90.

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 Using factor tree 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 ÷ 2 = 45 45 ÷ 3 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1 The prime factors of 90 are 2, 3, and 5. The prime factorization of 90 is: 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: 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.

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Problem 1

There are 9 teams and 90 players. How will they divide the players equally?

Okay, lets begin

Each team will get 10 players.

Explanation

To divide the players equally, we need to divide the total number of players by the number of teams. 90/9 = 10

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden 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 garden, we use the formula, Area = length × width 90 = 15 × width To find the value of the width, we need to shift 15 to the left side. 90/15 = width Width = 6.

Well explained 👍

Problem 3

There are 18 boxes and 90 chocolates. How many chocolates will be in each box?

Okay, lets begin

Each box will have 5 chocolates.

Explanation

To find the chocolates in each box, divide the total chocolates by the boxes. 90/18 = 5

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Problem 4

In a company, there are 90 employees, and 5 departments. How many employees are there in each department?

Okay, lets begin

There are 18 employees in each department.

Explanation

Dividing the employees by the total departments, we will get the number of employees in each department. 90/5 = 18

Well explained 👍

Problem 5

90 books need to be arranged in 5 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 18 books.

Explanation

Divide total books by shelves. 90/5 = 18

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FAQs on Factors of 90

1.What are the factors of 90?

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

2.Mention the prime factors of 90.

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

3.Is 90 a multiple of 9?

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 square 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: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 90 is 2 × 3² × 5. Sum of factors: The total when all factors of a number are added together. For example, the sum of the factors of 90 is 234.

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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.