Divisors of 40

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.

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 $\dfrac{40}{n}$ 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 = 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

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

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

$=15 \times 6=90$

(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

=40⁴

=40⁴

Related Topics:

• Divisors of numbers
• Factors of 40

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.