The divisors of 40 are those numbers that completely divide 40 without a remainder. In this section, we will discuss about the divisors of 40.

Table of Contents

## Highlights of Divisors of 40

- Divisors of 40: 1, 2, 4, 5, 8, 10, 20 and 40
- Negative divisors of 40: -1, -2, -4, -5, -8, -10, -20 and -40
- Prime divisors of 40: 2 and 5
- Number of divisors of 40: 8
- Sum of divisors of 40: 90
- Product of divisors of 40: 40
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## What are Divisors of 40

A number n is a divisor of 40 if $\dfrac{40}{n}$ is an integer. Note that if 40/n=m is an integer, then both m and n will be the divisors of 40.

To find the divisors of 40, we need to find the numbers n such that 40/n becomes an integer. We have:

40/1=40 | 1, 40 are divisors of 40. |

40/2=20 | 2, 20 are divisors of 40 |

40/4=10 | 4, 10 are divisors of 40 |

40/5=8 | 5, 8 are divisors of 40 |

No numbers other than 1, 2, 4, 5, 8, 10, 20, and 40 can divide 40. So we conclude that

The divisors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40. |

Thus, the total number of divisors of 40 is eight.

## Negative Divisors of 40

We know that if m is a divisor of a number, then -m is also a divisor of that number. As the divisors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40, we can say that:

The negative divisors of 40 are -1, -2, -4, -5, -8, -10, -20, and –40.

## Prime Divisors of 40

The divisors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Among these numbers, only 2 and 5 are prime numbers. So we obtain that:

The prime divisors of 40 are 2 and 5.

Video solution of Divisors of 40:

## Sum, Product & Number of Divisors of 40

The prime factorization of 40 is given below.

40 = 2^{3} × 5^{1}

(i) By the number of divisors formula, we have that the number of divisors of 40 is

=(3+1)(1+1)=4×2=8.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 40 is

$=\dfrac{2^4-1}{2-1} \times \dfrac{5^2-1}{5-1}$

$=\dfrac{16-1}{1} \times \dfrac{25-1}{4}$

$=15 \times 6=90$

(iii) By the product of divisors formula, we have that the product of the divisors of 40 is

=40^{(Number of divisors of 40)/2}

=40^{8}^{/2}

=40^{4}

=40^{4}

**Related Topics:**

## Question-Answer on Divisors of 40

**Question 1:** How many positive divisors do 40 have?

*Answer:*

40 has 8 positive divisors.

**Question 2:** What is the highest divisor of 40?

*Answer: *

40 is the highest divisor of 40.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.