A number is said to be a divisor of 38 if that number completely divides 38 with the remainder zero. In this section, we will discuss about divisors of 38.
Table of Contents
Highlights of Divisors of 38
- Divisors of 38: 1, 2, 19 and 38
- Negative divisors of 38: -1, -2, -19 and -38
- Prime divisors of 38: 2 and 19
- Number of divisors of 38: 4
- Sum of divisors of 38: 60
- Product of divisors of 38: 382
What are Divisors of 38
A number n is a divisor of 38 if $\dfrac{38}{n}$ is an integer. Note that if 38/n=m is an integer, then both m and n will be the divisors of 38.
To find the divisors of 38, we need to find the numbers n such that 38/n becomes an integer. We have:
| 38/1=38 | 1, 38 are divisors of 38. |
| 38/2=19 | 2, 19 are divisors of 38 |
No numbers other than 1, 2, 19, and 38 can divide 38. So we conclude that
|
The divisors of 38 are: 1, 2, 19, and 38. |
Thus, the total number of divisors of 38 is four.
Negative Divisors of 38
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 38 are 1, 2, 19, and 38, we can say that:
The negative divisors of 38 are -1, -2, -19, and –38.
Prime Divisors of 38
The divisors of 38 are 1, 2, 19, and 38. Among these numbers, only 2 and 19 are prime numbers. So we obtain that:
The prime divisors of 38 are 2 and 19.
Video solution of Divisors of 38:
Sum, Product & Number of Divisors of 38
The prime factorization of 38 is given below.
38 = 21 ×191
(i) By the number of divisors formula, we have that the number of divisors of 38 is
=(1+1)(1+1)=2×2=4.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 38 is
$=\dfrac{2^2-1}{2-1} \times \dfrac{19^2-1}{19-1}$
$=\dfrac{4-1}{1} \times \dfrac{361-1}{18}$
$=3 \times 20=60$
(iii) By the product of divisors formula, we have that the product of the divisors of 38 is
=38(Number of divisors of 38)/2
=384/2
=382
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