Question

What is the sum of the divisors of 42?

Answer 1

Hint: To find the sum of divisors of 42, first of all find the divisors of 42. Divisors of 42 can be found by writing all the factors of 42. $1,2,3,6,7,14,21,42$ are the factors of 42. Hence, adding them will give us the sum of the divisors of 42.

Complete step-by-step solutions:
In this question, we have to find the sum of the divisors of the number 42. That means, if 42 has 4 divisors then we have to find the sum of those 4 numbers.Now, what are divisors?

Divisors are those numbers that divide the given number completely and leave remainder zero.
Method to find the divisors of 42:
Write down all the factors of given number.
So, the factors of 42 are,
$$\begin{gathered} \Rightarrow 1\times 42=42 \\ \Rightarrow 2\times 21=42 \\ \Rightarrow 3\times 14=42 \\ \Rightarrow 6\times 7=42 \end{gathered}$$
Here, 1 divides 42 completely and leaves remainder 0.
2 divides 42 completely and leaves remainder 0.
3 divides 42 completely and leaves remainder 0.
6 divides 42 completely and leaves remainder 0.
7 divides 42 completely and leaves remainder 0.
14 divides 42 completely and leaves remainder 0.
21 divides 42 completely and leaves remainder 0.
42 divides 42 completely and leaves remainder 0.
Hence, all these numbers are the divisors of 42.
Therefore, we have found the divisors of 42, but according to our question, we need to find their sum.
So, adding all these numbers, we will get
Sum of divisors of 42$=1+2+3+6+7+14+21+42=96$

Hence, the sum of the divisors of 42 is 96.

Note: Note that factors and divisors are not the same. There is a difference between them. The divisors of a number other than 1 and the number itself are called factors and the given number and 1 are called divisors. For example Divisors of 42 are: $1,2,3,6,7,14,21,42$. Here, $2,3,6,7,14,21$ are the factors of 42 and 1, 42 are the divisors of 42. From the above explanation, we can conclude that all the factors are divisors but not all divisors are factors.