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.
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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