Factors of 9
2026-02-28 17:58 Diff
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Last updated on December 11, 2025

A number which divides another number exactly without leaving any remainder is called a factor of the given number. Factors play an important role in many real-life situations. They are useful in deciding the best time to schedule work shifts and events.

What are the Factors of 9?

Factors often come in pairs. There are several methods to figure them out, which you'll be learning about in a second. For now, let's just focus on the factors of 9, which are mentioned below:


Negative factors of 9: -1, -3, -9
Prime factors of 9:  3
Prime factorization of 9:  32
The sum of factors of 9:  1 + 3 + 9 = 13
 

How to Find the Factors of 9?

For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:

  • Use of Multiplication Method
  • Use of Division Method
  • Use of Prime Factors and Prime Factorization.

So, here we discuss a detailed explanation of the following methods:
 

Finding Factors Using Multiplication Method

 In the multiplication method, we will try to find out what numbers will multiply together, and give us the value 9. We will check the factors step by step:


Step 1: Start to multiply with numbers, which gives the value of 9.


Start with 1, and continue to multiply with other numbers. 


1 × 9 = 9
3 × 3 = 9


Step 2: After the calculation, we get these numbers, the factors of 9.


Step 3: The positive factor pairs of 9 found through multiplication are (1,9) and  (3,3)


Step 4: The negative factor pairs of 9 are (-1,-9), and (-3,-3)
 

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Finding Factors Using Division Method

Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 9:


Step 1: Divide 9 by smaller numbers and see if there is any remainder. E.g., 9/1 = 9. 


Step 2: We will continue in the same way and check for other numbers as well. For 9, the factors are 1, 3, and 9. Because 9 can be divided evenly by these numbers.
 

Prime Factors and Prime Factorization

The prime factor of 9 is 3. The prime factors can be found using the methods given below:

  • Prime Factorization
  • Factor Tree

By Using Prime Factorization: It is a method in which we break down a number into its prime factors. 

2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.


9÷3 = 3
3÷3 = 1


 The prime factorization of 9 is :


 9 = 32


With prime factorization, 9 can be broken down into prime factors of 3.
 

Using Factor Tree

A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find out the factors of any number.


Step 1: 9 divided by 3 gives us the quotient 3.


Step 2: Since 3 is a prime number, it cannot be divided further.


 The prime factorization of 9 is written below : 


 9 = 32
 

Factor Pairs

Every number has either a positive or negative factor. Let us look at those sets of factors.


Positive Pair Factors: (1,9), (3,3)
Negative Pair Factors: (-1, -9), (-3, -3)
 

Common Mistakes and How to Avoid Them in Factors Of 9

Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
 

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Problem 1

A chef made a cake that was 9 inches in diameter. He wants to cut that cake into 3 equal pieces. How to cut that equally?

Okay, lets begin

 Yes, the cake can be cut into 3 equal parts.
 

Explanation

The chef can cut the 9-inch cake into 3 parts of 3 inches each.
9 ÷ 3 = 3, no remainder. 
 

Well explained 👍

Problem 2

A tailor has a piece of cloth 9 meters long. He wants to cut that into 1-meter pieces. To find out how many pieces he will have.

Okay, lets begin

Yes, he will have 9 pieces.
 

Explanation

 He can easily cut the cloth. If he cut that cloth into 1-meter pieces, 
 9 ÷ 1 = 9 pieces, so he will have 9 pieces of cloth.
 

Well explained 👍

Problem 3

A teacher needs to create dance groups. She has 9 girls and wants to organize them into 3 dancers each. Help her to organize the teams, and how many teams can she form?

Okay, lets begin

The dance teacher can form 3 teams.
 

Explanation

Yes, she can create 3 teams, while she divides the 9 girls into teams of 3, she gets 3 teams. Here, 9 ÷ 3 = 3, so she can create 3 teams of 3 girls each.
 

Well explained 👍

FAQs on Factors Of 9

1.What is the factor tree of 9?

The factor tree of 9 visually represents the prime factors in a branching diagram. The prime factorization is visually represented using the factor tree.

2.Does 9 have exactly 2 factors?

No, 9 has 3 factors. The factors of 9 are 1, 3, and 9. 
 

3.Is 7 a factor of 9?

No, 7 is not a factor of 9 because 7 cannot be completely divided by 9.

4.Is 9 prime or composite?

9 is a composite number. A composite number will have more than two factors, and number 9 has 3 factors.

5.Is 9 a factor of 40?

No, 9 is not a factor of 40. The factors of 40 are: 1, 2, 4, 5, 8, 10, 20 and 40.
 

Important Glossaries For Factors Of 9

  • Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.
  • Prime Factors: Prime factors of a number are a set of prime numbers that multiply together to give the original number. For 9, 3 is the only prime factor.
  • Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
     

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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.