Question

Check whether the following number is divisible by $3$ (using rule)? Verify by actual division.

$12345$

Accepted Answer

Given,

$12345$

We need to divide this number by $3$ ,

The process of checking whether a number is divisible by a given number or not without actual division is called the divisibility rule for that number.

If the sum of the digits of a number is a multiple of $3$ , then that number is divisible by $3$ .

Let's take $12345$ and check,

$\Rightarrow 1 + 2 + 3 + 4 + 5$

$\Rightarrow 15$

Let's divide by $3$ to the above sum, we get,

$\Rightarrow \frac{15}{3}$

$\Rightarrow 5$

Now verify with actual division,

$\begin{matrix} 4 & 1 & 1 & 5 \\ 3 & 1 & 2 & 3 & 4 & 5 \\ 1 & 2 & ↓ & ↓ & ↓ \\ 0 & 0 & 3 & ↓ & ↓ \\ - & 3 & ↓ & ↓ \\ 0 & 4 & ↓ \\ - & 3 & ↓ \\ 1 & 5 \\ - & 1 & 5 \\ 0 & 0 \end{matrix}$

Therefore, we can see that the given number is divisible by $3$ .

Andhra Pradesh Board Solutions for Chapter: H.C.F and L.C.M, Exercise 2: CHECK YOUR PROCESS

Andhra Pradesh Board Mathematics Solutions for Exercise - Andhra Pradesh Board Solutions for Chapter: H.C.F and L.C.M, Exercise 2: CHECK YOUR PROCESS

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