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.
Table of Contents
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.
Video solution of Divisors of 39:
Sum, Product, Number of Divisors of 39
The prime factorization of 39 is given below.
39 = 31 ×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
$=\dfrac{3^2-1}{3-1} \times \dfrac{13^2-1}{13-1}$
$=\dfrac{9-1}{2} \times \dfrac{169-1}{12}$
$=4 \times 14=56$
(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
Related Topics:
FAQs on Divisors of 39
Answer: The divisors of 39 are 1, 3, 13, and 39.
Answer: The prime divisors of 39 are 3 and 13.
