Divisors of 21

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 $\frac{21}{n}$ 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.

 

Key Things

The prime factorization of 21 is given below.

21 = 3×71

(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

$=\frac{3^2-1}{3-1} \times \frac{7^2-1}{7-1}$

$=\frac{9-1}{2} \times \frac{49-1}{6}$

$=4 \times 8=32$

(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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