Question

Write the smallest digit and the greatest digit in the blank space of the following number so that the number formed is divisible by $$3$$.
$$4765$$_$$2$$.

Answer 1

Sum of the remaining digits$$=24$$
To make the number divisible by $$3$$, the sum of its digits should be divisible by $$3$$. As $$24$$ is already divisible by $$3$$, the smallest number that can be placed here is $$0$$.
Now, $$0+3=3$$
$$3+3=6$$
$$3+3+3=9$$
How ever, $$3+3+3+3=12$$
If we put $$9$$, then the sum of the digits will be $$33$$ and as $$33$$ is divisible by $$3$$, the number will also be divisible by $$3$$.
Therefore, the largest number is $$9$$.