Divisors of 38

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 $\frac{38}{n}$ 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.

 

Key Things

The prime factorization of 38 is given below.

38 = 2×191

(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

$=\frac{2^2-1}{2-1} \times \frac{19^2-1}{19-1}$

$=\frac{4-1}{1} \times \frac{361-1}{18}$

$=3 \times 20=60$

(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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