Question

The Roman numeral for \[3721\div 61\] is:
(a) LC
(b) XLI
(c) LXI
(d) CM

Answer 1

Hint: To solve the given question, we will first find out the value of \[3721\div 61.\] Now, we will write the number obtained after division as the sum of 100, 50, 10, 5, 1, etc. Then we will write 100 as C, 50 as L, 10 as X, 5 as V and 1 as I. Then, at last, we will arrange them in the descending order.

Complete step by step solution:
Before we solve this question, we must know what Roman Numeration System is. In Roman Numeration System, the natural numbers are written in the form of Latin alphabets like V, X, D, L, C, etc. Now, we have to find the Roman Numeral for \[3721\div 61.\] First, we have to find the value of \[3721\div 61.\] This value can be found out by the division method as shown.
\[61\overset{61}{\overline{\left){\begin{align}
  & \text{ }3721 \\
 & \underline{-366} \\
 & 61 \\
 & \underline{-61} \\
 & \text{ }0 \\
\end{align}}\right.}}\]
In the above division, we have used,
\[\begin{align}
  & 61\times 6=366 \\
 & 61\times 1=61 \\
\end{align}\]
Now, we will find the Roman Numeral of 61. For this, we will write 61 as the sum of 50, 10, 5, and 1. Thus, we can say that, 61 = 50 + 10 + 1.
Now, the Roman form of 50 is L, the Roman form of 10 is X and the Roman form of 1 is I. Thus, we can say that,
\[\Rightarrow 61=\left( L \right)+\left( X \right)+\left( I \right)\]
\[\Rightarrow 61=LXI\]
Hence, option (c) is the right answer.

Note: The order in which we write these alphabets is very important. The order should be descending i.e. the highest number should be on the left-hand side. As an example, option (b) has also the same elements but their order is different. It is not completely wrong to write in another order as the number obtained from option (b) will be 41. The X before L is used for subtracting and not adding.