Question

The smallest four digit number $\text{7\_86}$ is

Case I: exactly divisible by 9.

The digit that fits in the blank space is .

Case II: exactly divisible by 3.

The digit that fits in the blank space is .

Answer 1

Case I:

Divisibility by 9: Sum of all the digits should be divisible by 9.

Let the hundredths digit be $d$ in the number $7$_$86$.
Hence, $7+d+8+6=21+d$

The smallest digit $d$ that can make $21+d$ divisible by 9 is 6 as
$\Rightarrow 21+6=27$
which is divisible by 9.
$\therefore d=6$

Case II:

Divisibility by 3: Sum of all the digits should be divisible by 3.

Let the hundredths digit be $d$ in the number $7$_$86$.

Hence, $7+d+8+6=21+d$

$21$ is itself divisible by $3$
So, $d=0$