# Divisors of 39

A number is said to be a divisor of 39 if that number completely divides 39 without a remainder. In this section, we will discuss about divisors of 39.

#### Highlights of Divisors of 39

• Divisors of 39: 1, 3, 13 and 39
• Negative divisors of 39: -1, -3, -13 and -39
• Prime divisors of 39: 3 and 13
• Number of divisors of 39: 4
• Sum of divisors of 39: 56
• Product of divisors of 39: 392

#### What are Divisors of 39

A number n is a divisor of 39 if $\frac{39}{n}$ is an integer. Note that if 39/n=m is an integer, then both m and n will be the divisors of 39.

To find the divisors of 39, we need to find the numbers n such that 39/n becomes an integer. We have:

 39/1=39 1, 39 are divisors of 39. 39/3=13 3, 13 are divisors of 39

No numbers other than 1, 3, 13 and 39 can divide 39. So we conclude that

 The divisors of 39 are: 1, 3, 13 and 39.

Thus, the total number of divisors of 39 is four.

#### Negative Divisors of 39

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

As the divisors of 39 are 1, 3, 13, and 39, we can say that:

The negative divisors of 39 are -1, -3, -13, and –39.

#### Prime Divisors of 39

The divisors of 39 are 1, 3, 13, and 39. Among these numbers, only 3 and 13 are prime numbers. So we obtain that:

The prime divisors of 39 are 3 and 13.

Key Things

The prime factorization of 39 is given below.

39 = 3×131

(i) By the number of divisors formula, we have that the number of divisors of 39 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 39 is

$=\frac{3^2-1}{3-1} \times \frac{13^2-1}{13-1}$

$=\frac{9-1}{2} \times \frac{169-1}{12}$

$=4 \times 14=56$

(iii) By the product of divisors formula, we have that the product of the divisors of 39 is

=39(Number of divisors of 39)/2

=394/2

=392

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