The divisors of 9 are those numbers that completely divide 9 with the remainder zero. In this section, we will discuss about divisors of 9.

Table of Contents

## Highlights of Divisors of 9

- Divisors of 9: 1, 3 and 9
- Negative divisors of 9: -1, -3 and -9
- Prime divisors of 9: 3
- Number of divisors of 9: 3
- Sum of divisors of 9: 13
- Product of divisors of 9: 9
^{3/2 }=27.

## What are Divisors of 9

A number n is a divisor of 9 if $\dfrac{9}{n}$ is an integer. Note that if 9/n=m is an integer, then both m and n will be the divisors of 9.

Note that we have:

9/1=9 | 1, 9 are divisors of 9. |

9/3=3 | 3 is a divisor of 9 |

No numbers other than 1, 3, and 9 can divide 9. So we conclude that

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

Thus, the total number of divisors of 9 is three.

## Negative Divisors of 9

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 9 are 1, 3, and 9, we can say that:

The negative divisors of 9 are -1, -3, and –9.

## Prime Divisors of 9

The divisors of 9 are 1, 3, and 9. Among these numbers, only 3 is a prime number. So we obtain that:

The only prime divisor of 9 is 3.

Video solution of Divisors of 9:

## Sum, Product & Number of Divisors of 9

The prime factorization of 9 is given below.

9 = 3^{2}

(i) By the number of divisors formula, we have that the number of divisors of 9 is

=(2+1)=3.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 9 is

$=\dfrac{3^3-1}{3-1}$

$=\dfrac{27-1}{2}$

$=13$

(iii) By the product of divisors formula, we have that the product of the divisors of 9 is

=9^{(Number of divisors of 9)/2}

=9^{3/2}

=27

**Related Topics:**

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.