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.
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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