Question

Is 144 a multiple of 9? Give reasons.

Answer 1

Hint: In this question, we are asked whether 144 is a multiple of 9 or not. Or, whether 144 is completely divisible by 9 or not. There are many approaches to answer this question. Use the divisibility rule to answer. A number is said to be divisible by 9 if the sum of its digits is divisible by 9. Find the sum of the digits of 144. If the sum is divisible, the number is divisible, otherwise not.

Complete step-by-step answer:
There are multiple ways to solve this question. Let us look at a few of them.
Using the method solving by divisibility rule:
The divisibility rule of 9 says that the sum of the digits of the number should be divisible by 9.
For example: Let’s take a number- $94356$
Sum of the digits = $9 + 4 + 3 + 5 + 6 = 27$
Now since 27 is divisible by 9, the number $94356$ is also divisible by 9.
Now, we will use this method to find whether 144 is a multiple of 9 or not.
Sum of the digits= $1 + 4 + 4 = 9$

Since 9 is divisible by itself, 144 is also divisible by 9.

Note: The another way of solution,
Using the method finding factors of the given number.
In this method, we will simply find the factors of $144$ and check whether the factors are making $9$ or not.
$ \Rightarrow 144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3$
$ \Rightarrow 144 = {2^4} \times {3^2}$
We know that ${3^2} = 9$ and ${3^2}$ is also a factor of $144$. Therefore, 144 is divisible by 9.
3) Simply dividing.
To find whether 144 is a multiple of 9 or not, we can simply divide 144 by 9 and check. If the remainder is 0, then 144 is divisible by 9.
$ \Rightarrow 144 = 9 \times 16 + 0$ (written in the format- ${\text{Dividend}} = {\text{Divisor}} \times {\text{Quotient}} + {\text{Remainder}}$
Since the remainder is 0, 144 is divisible by 9.