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

Answer 1

Hint:If the sum of the digits of a number is divisible by 3, then the number is divisible by 3 which is called the divisibility rule of 3. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Given number 4765_2
It is given that the number is divisible by 3.
By the divisibility rule of 3, any number is divisible by 3, if the sum of its digits is divisible by 3.
Let the digit on the blank space be \[b\].
\[
   \Rightarrow 4 + 7 + 6 + 5 + b + 2 \\
   \Rightarrow b + 24 \\
\]
Here we can see that 24 is divisible by 3 as \[\dfrac{{24}}{3} = 8{\text{ times}}\]
Therefore, in order to make the required number divisible by 3, the least value of \[b\]is zero i.e., \[b = 0\].
If \[b = 0\], then \[4 + 7 + 6 + 5 + 0 + 2 = 24\] which is divisible by 3.
Thus, the number becomes 476502.
In order to make the required number divisible by 3, the greatest value of \[b\] is nine i.e., \[b = 9\].
If \[b = 9\], then \[4 + 7 + 6 + 5 + 9 + 2 = 33\] which is divisible by 3.
Thus, the number becomes 476592.
Hence, the smallest digit is 0 and the greatest digit is 9.

Note: As digit is a single number from 0 to 9, our obtained answer will lie between 0 to 9 only. We can also find the blank by substituting each digit in it and verifying by the divisibility rule of 3.