Question

How do you write the remainder when 998 is divided by 37?

Answer 1

Hint: To divide larger numbers we will use a long division method. Long division moves from left to right. Here 998 is the dividend, 37 is the divisor and we have to find the quotient. By using the long division method we will get the desired answer.

Complete step-by-step solution:
We have to find the remainder when 998 is divided by 37.
Now, we know that to solve larger divisions, the long division method is the best choice. We will solve the given division by using a long division method.
Now, let us start dividing the terms by long division method. Then we will get
\[37\overset{26}{\overline{\left){\begin{align}
  & 998 \\
 & \underline{74} \\
 & 258 \\
 & \underline{222} \\
 & 36 \\
\end{align}}\right.}}\]
Hence on dividing 998 by 37 we get the quotient as 26 and remainder as 36.

Note: The possibility of mistake while solving the question is that when we start dividing the terms from left to right we have to consider the number from left which is greater than the divisor. If we get the number less than the divisor at any step than we must have to add zero in the quotient. In this question we get 36 which is less than 37 but there is no other number left in the dividend so there is no need to add zero in the quotient. We can also check our answer by using the formula that $\text{Dividend=quotient}\times \text{divisor+remainder}\text{.}$.
Substituting the values we will get
$\Rightarrow 998\text{=26}\times 37\text{+36}\text{.}$
Simplifying the above obtained equation we will get
$\Rightarrow 998\text{=998}$
Hence the required answer is correct.