Question

A number is divisible by $8$, by what other numbers will that number be divisible?

Answer 1

Hint: In this question we have been asked to find the numbers that will divide a number which is divisible by $8$. In these types of questions there is no such particular formula. For this we need to revise the definition of factors. We can also understand the divisibility rule of $8$ and find the numbers.

Complete step by step answer:
We know that the divisibility rule of eight says that” If the number formed by the last three digits of a number is divisible by $8$, then that particular number is also divisible.We have been given that a number is divisible by $8$.

Let us assume that number is $X$. When we say that a number is divisible by another, we mean that on division the remainder is Zero. We can write it as $\dfrac{X}{8}$, then the remainder is $0$.
Since the above statement is true, then it is true for all factors of $8$.
Factors of eight are $1,2,4,8$. This is true for all cases. So we can say that $\dfrac{X}{1},\dfrac{X}{2},\dfrac{X}{4},\dfrac{X}{8}$, the remainder is $0$.
Thus we can say that $X$ is divisible by $1,2,4$ other than $8$.

Hence if the number is divisible by $8$, then it is also divisible by $1,2$ and $4$.

Note: Let us take an example , a number $30248$. Now the last three numbers are $248$, it is divisible by $8$. This can also be written as $248 = 31 \times 8$. So according to the divisibility of $8$, the number $30248$ is divisible by $8$. So this number is also divisible by $1,2,4$. We can check this as $\dfrac{{30248}}{2} = 15124\,\Rightarrow\,\dfrac{{30248}}{4} = 7562$. So we can also confirm this method.