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
 

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:
 

 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)
 

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.
 

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.
 

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
 

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)
 

• 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).