A number is said to be a divisor of 21 if that number completely divides 21 with the remainder zero. In this section, we will discuss about divisors of 21.
Table of Contents
Highlights of Divisors of 21
- Divisors of 21: 1, 3, 7 and 21
- Negative divisors of 21: -1, -3, -7 and -21
- Prime divisors of 21: 3 and 7
- Number of divisors of 21: 4
- Sum of divisors of 21: 32
- Product of divisors of 21: 212
What are Divisors of 21
A number n is a divisor of 21 if $\dfrac{21}{n}$ is an integer. Note that if 21/n=m is an integer, then both m and n will be the divisors of 21.
To find the divisors of 21, we need to find the numbers n such that 21/n becomes an integer. We have:
| 21/1=21 | 1, 21 are divisors of 21. |
| 21/3=7 | 3, 7 are divisors of 21 |
No numbers other than 1, 3, 7, and 21 can divide 21. So we conclude that
|
The divisors of 21 are: 1, 3, 7, and 21. |
Thus, the total number of divisors of 21 is four.
Negative Divisors of 21
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 21 are 1, 3, 7, and 21, we can say that:
The negative divisors of 21 are -1, -3, -7, and –21.
Prime Divisors of 21
The divisors of 21 are 1, 3, 7, and 21. Among these numbers, only 3 and 7 are prime numbers. So we obtain that:
The prime divisors of 21 are 3 and 7.
Video solution of Divisors of 21:
Sum, Product & Numbers of Divisors of 21
The prime factorization of 21 is given below.
21 = 31 ×71
(i) By the number of divisors formula, we have that the number of divisors of 21 is
=(1+1)(1+1)=2×2=4.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 21 is
$=\dfrac{3^2-1}{3-1} \times \dfrac{7^2-1}{7-1}$
$=\dfrac{9-1}{2} \times \dfrac{49-1}{6}$
$=4 \times 8=32$
(iii) By the product of divisors formula, we have that the product of the divisors of 21 is
=21(Number of divisors of 21)/2
=214/2
=212
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