Factors of 9

Factors of 9 are 1, 3, and 9 itself. If any of the numbers divide the provided number 9, without leaving any remainder, that will be the factor of 9. Suppose we have integer 2 that does not divide 9 and leaves the remainder as well. At the same, we have another integer after 2 is 3, which divides 9 without leaving any remainder. So, Simply we can say it’s a factor of 9.

In this article, we will learn about several topics like factors of 9, pairs distribution in factors of positive and negative integers, and so on.

Factors Definition

Factors are numbers that divide another number exactly, without leaving a remainder.

For example, the factors of 6 are 1, 2, 3, and 6, as they divide 6 exactly.

What are the Factors of 9?

9 has three factors, that is, 1, 3 and 9.

The numbers that can be multiplied together to produce the product 9 are known as the factors of 9. The elements in the case of 9 are 1, 3, and 9. So, let’s do the Pairwise multiplication of these numbers to get 9:

• 1 × 9 = 9
• 3 × 3 = 9

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

Note: Sum of All Factors of 9 is 13 i.e., (1+3+9).

List of All Factors of 9

The entire list of 9 factors is as follows:

Factors of 9 are 1,3 and 9.

Prime Factors of 9

We must divide 9 by each prime number until there is only one remaining to get the prime factor of 9.

• Let’s divide it by the smallest prime factor which is 2, (9/2 = 4.5) we will get the answer in fraction form.
• After that, the smallest prime factor is 3. (9/3 = 3).
• By the same process, we will try it with various prime factors, At last, the number itself will be 9 only,(9/9 =1) and we get the remainder 1.
• But we can’t divide 1 by any prime factor, So therefore

Prime factors of 9 = 3 x 3 = 3².

Read More about Prime Numbers.

How to Find Factors of 9?

To find the Factors of 9 there are various methods such as Division Method or Prime Factorization method. We will discuss both of these methods in detail as follows:

Factors of 9 by Division Method

The integers that divide 9 evenly without leaving an excess can be found to be the factors of 9. Here let’s look at how you can achieve it:

• Every number is divisible by 1 and itself. So, we can say the factor of 9 are 1 and 9.
• Now, let’s look at another integer that will not leave any remainder as 3.
  Therefore, 3 × 3 = 9.
• So, Factors of 9 are 1,3 and 9.

Prime Factorization of 9

Prime factorization of factoring any integer using prime numbers because each number may be written as the product of prime numbers. So, let’s start dividing 9 by the smallest prime number, which is 3, and keep dividing until the remainder must be 1 or further division is impossible to obtain the prime factorization of 9, as follows:

Step 1: Start with 9.
Step 2: Divide by the smallest prime number, which is 3: 9÷3=3
Step 3: Divide by 3 again: 3÷3=1

Read More about Prime Factorization.

Factor Tree of 9

A factor tree is a diagram used to break down a number into its prime factors. For the number 9, the factor tree is quite simple, as 9 is not a large number. Here’s the illustration for Factor Tree of 9.

Factor Pairs of 9

Factor pairs are pairs of numbers that, when multiplied together, give a specific product. For any number there can be various factor pairs i.e., positive factor pairs and negative factor pairs. Let’s discuss the factor pair of 9 in detail.

Positive Factor Pair of 9

Multiply the two integers in a pair to obtain the original number, 9, to find the “Pair factors of Positive integers”:

• 1 × 9 = 9
• 3 × 3 = 9

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

Negative Factor Pair of 9

Now, Let’s Multiply the two integers in a pair to obtain the original number, 9, to find the “Pair factors of negative integers”:

• -1 × -9 = 9
• -3 × -3 = 9

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

Read More,

• Factor of 12
• Factor of 36

Factors of 9 – Solved Examples

Example 1: What is the sum of all the factors of 9?

Solution:

The factors of 9 are 1, 3 and 9

Sum of the factors of 9 = 1+3+9

Sum of the factors of 9 = 13

Example 2: What are the common factors of 9 and 27?

Solution:

Let’s find the factors of given number.

9 = 1, 3 and 9

27 = 1, 3, 9 and 27

Therefore, the common factors of 9 and 27 are 1, 3 and 9.

Example 3: Find two factors of 9 whose product equals 9.

Solution:

Listed are the factors of 9 are 1, 3 and 9

Two factors of 9 whose product is 9 are:

1 and 9

So, 1 × 9 = 9.

Example 4: Express 9 as the product of its prime factors.

Solution:

Here’s we will express 9 as the product of its prime factors:

• Start with 9.
• Divide by the smallest prime number, which is 3 (9÷3=3)
• Divide by 3 again (3÷3=1)

So, we can say that prime factorization 9 is 3 × 3.

Factors of 9 – Practice Questions

Q1: What is the product of the factors of 9?

Q2: Is 6 is a factor of 9.

Q3: Check if 5 is a factor of 9.

Q4: Niki was playing a math game with her friends. In the game, She was asked to find the factors of 9. So what will be the answer?

Factors of 9 – Frequently Asked Questions

Does 9 have only 3 factors?

Yes, 9 has three factors: 1, 3, and 9.

What is the Factor Tree of 9?

Factor tree of 9: 3 × 3 which is illustrated in the article above.

Is 9 a Factor of Itself?

Yes, 9 is a factor of itself.

What is the Prime Factorization of 9?

Prime factorization of 9 is 3 × 3.

What is the Factor of 9 from the Numbers 3, 4, 5, 6, 7, 8, and 9?

From numbers 3, 4, 5, 6, 7, 8, and 9; 3 and 9 are a factors of 9.

Why 9 is not a Prime Factor?

9 is not prime; it’s divisible by 1, 3, and 9.

What are the Common Factors of 9 and 15?

Common factors of 9 and 15 is 1 and 3.

What are Common Factors of 9 and 18?

Common Factors of 9 and 18 are 1, 3 and 9

What are Common Factors of 9 and 12?

Common Factors of 9 and 12 are 1 and 3