A number is said to be a divisor of 46 if that number completely divides 46 with the remainder zero. In this section, we will discuss about divisors of 46.
Table of Contents
Highlights of Divisors of 46
- Divisors of 46: 1, 2, 23 and 46
- Negative divisors of 46: -1, -2, -23 and -46
- Prime divisors of 46: 2 and 23
- Number of divisors of 46: 4
- Sum of divisors of 46: 72
- Product of divisors of 46: 462
What are Divisors of 46
A number n is a divisor of 46 if $\dfrac{46}{n}$ is an integer. Note that if 46/n=m is an integer, then both m and n will be the divisors of 46.
To find the divisors of 46, we need to find the numbers n such that 46/n becomes an integer. We have:
| 46/1=46 | 1, 46 are divisors of 46. |
| 46/2=23 | 2, 23 are divisors of 46 |
No numbers other than 1, 2, 23, and 46 can divide 46. So we conclude that
|
The divisors of 46 are: 1, 2, 23, and 46. |
Thus, the total number of divisors of 46 is four.
Negative Divisors of 46
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 46 are 1, 2, 23, and 46, we can say that:
The negative divisors of 46 are -1, -2, -23, and –46.
Prime Divisors of 46
The divisors of 46 are 1, 2, 23, and 46. Among these numbers, only 2 and 23 are prime numbers. So we obtain that:
The prime divisors of 46 are 2 and 23.
Video solution of Divisors of 46:
Sum, Product & Number of Divisors of 46
The prime factorization of 46 is given below.
46 = 21 ×231
(i) By the number of divisors formula, we have that the number of divisors of 46 is
=(1+1)(1+1)=2×2=4.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 46 is
$=\dfrac{2^2-1}{2-1} \times \dfrac{23^2-1}{23-1}$
$=\dfrac{4-1}{1} \times \dfrac{529-1}{22}$
$=\dfrac{3}{1} \times \dfrac{528}{22}$
$=3 \times 24=72$
(iii) By the product of divisors formula, we have that the product of the divisors of 46 is
=46(Number of divisors of 46)/2
=464/2
=462
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