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
=408/2
=404
=404
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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.