# Divisors of 40

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

#### 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: 404

#### What are Divisors of 40

A number n is a divisor of 40 if $\frac{40}{n}$ 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.

Key Things

The prime factorization of 40 is given below.

40 = 23 × 51

(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

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

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

$=15 \times 6=90$

(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

=408/2

=404

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