# Divisors of 46

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 $\frac{46}{n}$ 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.

Key Things

The prime factorization of 46 is given below.

46 = 2×231

(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

$=\frac{2^2-1}{2-1} \times \frac{23^2-1}{23-1}$

$=\frac{4-1}{1} \times \frac{529-1}{22}$

$=\frac{3}{1} \times \frac{528}{22}$

$=3 \times 24=72$

(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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