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.
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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