Definition of factors of 9: If a number completely divides 9 without leaving a remainder, then that number is called a factor of 9.

By the above definition, we can say that the factors of 9 are the divisors of 9. In this section, we will learn about the factors of 9 and the prime factors of 9.

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Table of Contents

## Highlights of Factors of 9

**9=3×3**is the prime factorization of 9.- The factors of 9 are 1, 3, and 9.
- The only prime factor of 9 is 3.
- Negative factors of 9 are –1, -3, and –9.

## What are the factors of 9?

Let us write the number 9 multiplicatively in all possible ways. We definitely have:

9 = 1×9

9 = 3×3

We cannot write 9 multiplicatively in any other way than the above ones, so we will stop right now. Thus the factors of 9 in pairs are given as follows:

9 = a×b | Factors in Pairs (a,b) |

9 = 1×9 | (1, 9) |

9 = 3×3 | (3, 3) |

Thus the pair factors of 9 are (1, 9) and (3, 3). As all the numbers appearing in pair factors are the factors of 9, we conclude that

The factors of 9 are: 1, 3, and 9. |

## Number of factors of 9

From above we have calculated the factors of 9 which are 1, 3, and 9. Thus the total number of factors of 9 is three.

## Prime Factors of 9

Note that the factors of 9 are 1, 3, and 9. Among those factors, we observe that only 3 is a prime number as 3 does not have any proper divisors.

∴ the only prime factor of 9 is 3.

Question: What are the factors of 9?

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## How to find factors of 9?

Now we will determine the factors of 9 by **division method**. In this method, we will try to find the numbers that can divide 9 with no remainder. See that

9/1=9 and the remainder is 0.

∴ 1 and 9 are factors of 9.

9/3=3 and the remainder is 0.

∴ 3 and 3 are factors of 9 ⇒ 3 is a factor of 9.

Note that no numbers other than the numbers in violet color can divide 9. So the numbers in violet color, that is, 1, 3, and 9 are the complete list of factors of 9.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.