Question

How do I find if a number is a multiple of $8$ or not.

Answer 1

Hint: Basically, we can say that, if we get a remainder as zero when we divide $x$ with $y$, then $x$ is the multiple of $y$. Mathematically $\dfrac{x}{y}=a\Leftrightarrow x\text{ is multiple of }y$. So, the simplest way to check whether the given number is multiple of $8$ or not is dividing the given number with the $8$ and calculating the remainder and checking whether the remainder is zero or not.

Complete step-by-step solution:
Let us consider a number $416$.
Dividing the above number with $8$, then we will get
$\dfrac{416}{8}=52$ and the remainder is equal to zero. So, we can say that the number $416$ is multiple of $8$. Now consider a number which is having more than three digits. Let’s say $23125208$.
Here we have eight digits and dividing the eight digit number is not an easy task. For this we need to use division rules. We have a division rule for $8$ as “In a number, if the number formed by the last three digits of the given number are divided by $8$, then the whole number is divided by $8$.”
So, while coming to the number $23125208$. The number formed by the last three digits is $208$. Dividing $208$ by $8$ then we will get $\dfrac{208}{8}=26$ and the remainder is zero. So, the number not only $23125208$ but also all the numbers which are having $208$ at the ending are divisible by $8$.


Note: Division rules are the set of rules to predict whether the given number is divisible by another number or not. We have division rules for $2,3,4,5,6,8,10,11,13.$ From these division rules, we can check whether the given number is multiple or divisible by a number.