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: 93/2 =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 = 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
$=\dfrac{3^3-1}{3-1}$
$=\dfrac{27-1}{2}$
$=13$
(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
=93/2
=27
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