A number is said to be a divisor of 42 if that number completely divides 42 with the remainder zero. In this section, we will discuss about divisors of 42.
Table of Contents
Highlights of Divisors of 42
- Divisors of 42: 1, 2, 3, 6, 7, 14, 21 and 42
- Negative divisors of 42: -1, -2, -3, -6, -7, -14, -21 and -42
- Prime divisors of 42: 2, 3 and 7
- Number of divisors of 42: 8
- Sum of divisors of 42: 96
- Product of divisors of 42: 424
What are Divisors of 42
A number n is a divisor of 42 if $\dfrac{42}{n}$ is an integer. Note that if 42/n=m is an integer, then both m and n will be the divisors of 42.
To find the divisors of 42, we need to find the numbers n such that 42/n becomes an integer. We have:
| 42/1=42 | 1, 42 are divisors of 42. |
| 42/2=21 | 2, 21 are divisors of 42 |
| 42/3=14 | 3, 14 are divisors of 42 |
| 42/6=7 | 6, 7 are divisors of 42 |
No numbers other than 1, 2, 3, 6, 7, 14, 21, and 42 can divide 42. So we conclude that
|
The divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42. |
Thus, the total number of divisors of 42 is eight.
Negative Divisors of 42
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42, we can say that:
The negative divisors of 42 are -1, -2, -3, -6, -7, -14, -21, and –42.
Prime Divisors of 42
The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Among these numbers, only 2, 3, and 7 are prime numbers. So we obtain that:
The prime divisors of 42 are 2, 3, and 7.
Video solution of Divisors of 42:
Sum, Product & Number of Divisors of 42
The prime factorization of 42 is given below.
42 = 21 × 31 ×71
(i) By the number of divisors formula, we have that the number of divisors of 42 is
=(1+1)(1+1)(1+1)=2×2×2=8.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 42 is
$=\dfrac{2^2-1}{2-1} \times \dfrac{3^2-1}{3-1} \times \dfrac{7^2-1}{7-1}$
$=\dfrac{4-1}{1} \times \dfrac{9-1}{2} \times \dfrac{49-1}{6}$
$=3 \times 4 \times 8=96$
(iii) By the product of divisors formula, we have that the product of the divisors of 42 is
=42(Number of divisors of 42)/2
=428/2
=424
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