Question

Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by $3$:

• A. $\_\_6724$
• B. $4765\_\_2$

Answer 1

Answer: (A), (B)

$4765\_\_2$

Determine the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by $3$:

According to the divisibility rule, a number is totally divisible by $3$ if the sum of its digits is divisible by $3$.

Explanation for Option A

$\_\_6724$

The sum of the digit $=4+2+7+6=19$
As a result, the smallest digit to be used is blank space $=2$.

So, the sum is $19+2=21$, which is divisible by $3$.

The greatest digit to fill in the blank space $=8$.

So, the sum is $19+8=27$, which is again divisible by $3$.

Therefore, the required digits are $2$ and$8$ .

Explanation for Option B

$4765\_\_2$
The sum of the digit $=2+5+6+7+4=24$
Therefore, the smallest digit to be inserted in the blank space$=0$.

So total remains same $24+0=24$, which is divisible by $3$.

The greatest digit to fill in the blank space is $9$.

The sum is $24+9=33$, which is divisible by $3$.
Therefore, the required digits are $0$ and $9$.

Hence, the smallest digit and the greatest digit so that the number formed is divisible by $3$ are (a) $2$ and$8$ (b) $0$ and $9$.