# Divisors of 33

A number is said to be a divisor of 33 if that number completely divides 33 without a remainder. In this section, we will discuss about divisors of 33.

#### Highlights of Divisors of 33

• Divisors of 33: 1, 3, 11 and 33
• Negative divisors of 33: -1, -3, -11 and -33
• Prime divisors of 33: 3 and 11
• Number of divisors of 33: 4
• Sum of divisors of 33: 48
• Product of divisors of 33: 332

#### What are Divisors of 33

A number n is a divisor of 33 if $\frac{33}{n}$ is an integer. Note that if 33/n=m is an integer, then both m and n will be the divisors of 33.

To find the divisors of 33, we need to find the numbers n such that 33/n becomes an integer. We have:

 33/1=33 1, 33 are divisors of 33. 33/3=11 3, 11 are divisors of 33

No numbers other than 1, 3, 11 and 33 can divide 33. So we conclude that

 The divisors of 33 are: 1, 3, 11 and 33.

Thus, the total number of divisors of 33 is four.

#### Negative Divisors of 33

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

As the divisors of 33 are 1, 3, 11, and 33, we can say that:

The negative divisors of 33 are -1, -3, -11, and –33.

#### Prime Divisors of 33

The divisors of 33 are 1, 3, 11, and 33. Among these numbers, only 3 and 11 are prime numbers. So we obtain that:

The prime divisors of 33 are 3 and 11.

Key Things

The prime factorization of 33 is given below.

33 = 3×111

(i) By the number of divisors formula, we have that the number of divisors of 33 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 33 is

$=\frac{3^2-1}{3-1} \times \frac{11^2-1}{11-1}$

$=\frac{9-1}{2} \times \frac{121-1}{10}$

$=4 \times 12=48$

(iii) By the product of divisors formula, we have that the product of the divisors of 33 is

=33(Number of divisors of 33)/2

=334/2

=332

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