Divisors of 22

The divisors of 22 are those numbers that completely divide 22 without a remainder. In this section, we will discuss about divisors of 22.

Highlights of Divisors of 22

  • Divisors of 22: 1, 2, 11 and 22
  • Negative divisors of 22: -1, -2, -11 and -22
  • Prime divisors of 22: 2 and 11
  • Number of divisors of 22: 4
  • Sum of divisors of 22: 36
  • Product of divisors of 22: 222 =484.

What are Divisors of 22

A number n is a divisor of 22 if $\frac{22}{n}$ is an integer. Note that if 22/n=m is an integer, then both m and n will be the divisors of 22.

To find the divisors of 22, we need to find the numbers n such that 22/n becomes an integer. We have:

22/1=22 1, 22 are divisors of 22.
22/2=11 2, 11 are divisors of 22

No numbers other than 1, 2, 11 and 22 can divide 22. So we conclude that

The divisors of 22 are:

1, 2, 11 and 22.

Thus, the total number of divisors of 22 is four.

 

Negative Divisors of 22

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 22 are 1, 2, 11, and 22, we can say that:

The negative divisors of 22 are -1, -2, -11, and –22.

 

Prime Divisors of 22

The divisors of 22 are 1, 2, 11, and 22. Among these numbers, only 2 and 11 are prime numbers. So we obtain that:

The prime divisors of 22 are 2 and 11.

 

Key Things

The prime factorization of 22 is given below.

22 = 21 × 111

(i) By the number of divisors formula, we have that the number of divisors of 22 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 22 is

$=\frac{2^2-1}{2-1} \times \frac{11^2-1}{11-1}$

$=\frac{4-1}{1} \times \frac{121-1}{10}$

$=3 \times 12=36$

(iii) By the product of divisors formula, we have that the product of the divisors of 22 is

=22(Number of divisors of 22)/2

=224/2

=222

=484

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