Question

Write the smallest digit and the greatest possible digit in the blank space of each of the following numbers so that the number formed is divisible by $3$$=4765{\_}_{}2$

Answer 1

The given number is $4765$ __ $2$ is divisible by 3.

By the divisibility rule of 3, any number is divisible by 3 if the sum of its digit is divisible by 3.

Let the digit on the blank space be $a$.

$4+7+6+5+a+2$

$\Rightarrow a+24$

In order to make required number divisible by 3 , the least value of $a$ is 0 and the maximum value of $a$ is 9.

If $a=0$, then $0+24=24$. This is divisible by 3.

If $a=9$, then $9+24=33$. This is divisible by 3.