Factors

# Factors of 9 | Prime Factorization of 9 | Factor Tree of 9

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 9 | Prime Factorization of 9 | Factor Tree of 9

When two numbers are multiplied together to get the result of 9, they are called factors of 9. The factors of 9 can be written in either positive or negative form. In this article, you will be learning about factors of 9 using the factor tree method, prime factorization method, and division method.

## What Are the Factors of 9?

The numbers that divide 9 without leaving any remainder are known as factors of 9. The factors can be represented in both positive and negative forms. Prime numbers and composite numbers are the two major classifications found in the factors of 9. Composite numbers are the numbers that have more than two factors while prime numbers have two or less than two factors. The number 9 is having more than two factors it can be called as the composite number and those factors are 1, 3, and 9.

## What Are the Factors of 9 in Pairs?

The factors of 9 can be both positive and negative. The combination of two numbers is called a pair factor of 9. When we multiply the pair factors of 9, the result will always be 9 and we will always get the original product.

## Positive Pair Factors of 9

The positive pair factors of 9 are (1, 9), and (3,3).

## Negative Pair Factors of 9

The negative pair factors of 9 are (-1, -9), and (-3,-3).

## How to Find Factors of 9 Through Division Method?

The numbers that divide 9 without leaving any remainder is known as the factors of 9. Through the division method, we can find the factors of 9 by a dividing sequence of numbers. The steps are as follows:

• 9 ÷ 1 = 9
• 9 ÷ 3 = 3
• 9 ÷ 9 = 1

Therefore, the factors of 9 are 1, 3, and 9.

## Prime Factorization of 9

Before applying the prime factorization method to find out the factors, you need to check whether the number 9 is a composite number or a prime number. Here, 9 is a composite number as it has more than two factors, as mentioned above. The steps of prime factorization method are as follows:

Step 1: Divide the number 9 by the smallest prime number that can divide evenly. That number is 3.
9 ÷ 3 = 3
Step 2: We get 3 as the quotient. Now, divide 3 by the smallest prime number which is 3.
3 ÷ 3 = 1
The final quotient is 1. Since it cannot be divided further, the prime factors of 9 are 3 x 3 x 1.
The prime factorization for 9 can be represented as below:

We can see that 3 is the number which do not leave any remainder when divided by 9. Thus they are the factors of 9.

## What Is the Factor Tree of 9?

The factor tree method can be used to find out the prime factors of 9. Let’s take 9 at the top of the factor tree. Then split the factors into factors and write down the set of the pair factors. This process is continued until the pair of factors turns into prime numbers. Finally, by identifying all the prime numbers we will get a prime factor of 9.The steps involved in the factor tree method are as follows:

Step 1: Let’s place the number 9 at the top and write down 9 in pairs, that is, 1 and 3.
Step 2: The branches in the factor tree will now be all the prime numbers.
Circling all the branches, 1 and 3, which are the prime factors of 9.
There are many ways in which we can write the factor tree of 9. Below is an image representation of the factor tree of 9, choosing 1 and 3 as pair factors of 9.

## Solved Examples of Factors of 9

What are the factors of 9?
The factors of 9 are 1, 3, and 9.

What are the positive and negative pairs of 9?
The positive factors of 9 are 1, 3, and 9 and the negative factors of 9 are -1, -3, and -9

What is the prime factor of 9?
The prime factor of 9 is 3.

What is the prime factorization of 9?
The Prime Factorization of 9: 3 x 3 x 1.

## Frequently Asked Questions

How many numbers are multiples of 9?
The first 10 multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.

Is 9 is a factor of 15?
No, 9 is not a factor of 15. As 15 is not divisible by 9.

Is 9 a factor of every number?
No, 9 is not a factor of every number. 9 is the factor of those numbers that are divisible by 9.

What are the factors of 9?
The factors of 9 are 1, 3, and 9.

What are the factors and multiples of 9?
The factors of 9 are 1, 3, and 9 and the first 10 multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.

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Written by by

Prerit Jain

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