Question

The least 3 digit number which is divisible by 7 is?

Answer 1

Hint: We know that the least three digit number that could be possible is 100 and when we divide 100 by 7 we get the remainder 2 so if we add 5 in 100 then the remainder when dividing 100 by 7 will be 0.
Hence, adding 5 to 100 will give the answer.

Complete step-by-step answer:
The smallest (or least) three digit number is 100. You might think 000 is the smallest 3 digit number because we know the order of the number 0 is the smallest but then we know if we put 0 in front of a number then it has no meaning and as we need a 3 digit number so the number just greater than 0 is 1 so we put 1 in the hundreds place and 0 in the tens and units place.
Now, if we divide this smallest three digit number 100 by 7 we get,
\[7\overset{14}{\overline{\left){\begin{align}
  & 100 \\
 & \dfrac{7}{\begin{align}
  & 30 \\
 & \dfrac{28}{2} \\
\end{align}} \\
\end{align}}\right.}}\]
From the above division, you can see that the remainder is 2 so to make the remainder 0 when the number is divisible by 7 add 5 to 100 i.e. 105 when divided by 7 gives 0 as a remainder.
\[7\overset{15}{\overline{\left){\begin{align}
  & 105 \\
 & \dfrac{7}{\begin{align}
  & 35 \\
 & \dfrac{35}{00} \\
\end{align}} \\
\end{align}}\right.}}\]
Hence, the least 3 digit number divisible by 7 is 105.

Note: You might have thought that why we chose 105 as a three digit number because we have asked to find the least three digit number which is divisible by 7 and after 100, the least three digit number divisible by 7 is 105.
You might have also thought that 101 could be a smallest three digit number which is divisible by 7 but when you divide 101 by 7, you will get the remainder 3. Similarly, when you can check divisibility of 7 for 102, 103, 104 you will find that the remainder is not 0.