# Divisors of 27

A number is said to be a divisor of 27 if that number completely divides 27 without a remainder. In this section, we will discuss about divisors of 27.

#### Highlights of Divisors of 27

• Divisors of 27: 1, 3, 9 and 27
• Negative divisors of 27: -1, -3, -9 and -27
• Prime divisors of 27: 3
• Number of divisors of 27: 4
• Sum of divisors of 27: 40
• Product of divisors of 27: 272

#### What are Divisors of 27

A number n is a divisor of 27 if $\frac{27}{n}$ is an integer. Note that if 27/n=m is an integer, then both m and n will be the divisors of 27.

To find the divisors of 27, we need to find the numbers n such that 27/n becomes an integer. We have:

 27/1=27 1, 27 are divisors of 27. 27/3=9 3, 9 are divisors of 27

No numbers other than 1, 3, 9 and 27 can divide 27. So we conclude that

 The divisors of 27 are: 1, 3, 9 and 27.

Thus, the total number of divisors of 27 is four.

#### Negative Divisors of 27

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

As the divisors of 27 are 1, 3, 9, and 27, we can say that:

The negative divisors of 27 are -1, -3, -9, and –27.

#### Prime Divisors of 27

The divisors of 27 are 1, 3, 9, and 27. Among these numbers, only 3 is a prime number. So we obtain that:

The only prime divisor of 27 is 3.

Key Things

The prime factorization of 27 is given below.

27 = 33

(i) By the number of divisors formula, we have that the number of divisors of 27 is

=(3+1)=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 27 is

$=\frac{3^4-1}{3-1}$

$=\frac{81-1}{2}$

$=40$

(iii) By the product of divisors formula, we have that the product of the divisors of 27 is

=27(Number of divisors of 27)/2

=274/2

=272

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