# Divisors of 9

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.

#### 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: 93/2 =27.

#### What are Divisors of 9

A number n is a divisor of 9 if $\frac{9}{n}$ 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.

Key Things

The prime factorization of 9 is given below.

9 = 32

(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

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

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

$=13$

(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

=93/2

=27

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