Question

Find the sum of remainder obtained when 64, 65 and 66 are divided by 7.

Answer 1

Hint: Type of question is particularly based on the division. As in the question it is asked to find out the sum of remainder we will get after dividing the numbers 64, 65 and 66 by 7. So we just need to simply divide the numbers by 7 one by one and then add their remainder to get the answer. So as we know that remainder is an amount left after the division.

Complete step by step answer:
So moving ahead with the question, let us first divide the number 64 by 7. So we will get;
\[7\overset{9}{\overline{\left){\begin{align}
  & 64 \\
 & \underline{63} \\
 & 01 \\
\end{align}}\right.}}\]
So we will get remainder 1; i.e. $64\div 7=7\times 9+1$.
Similarly calculating the remainder for the number 65 when divided by number 7. So we will get;
\[7\overset{9}{\overline{\left){\begin{align}
  & 65 \\
 & \underline{63} \\
 & 02 \\
\end{align}}\right.}}\]
So we will get the remainder 2; i.e. $65\div 7=7\times 9+2$.
Similarly calculating the remainder for the number 66 when divided by number 7. So we will get;
\[7\overset{9}{\overline{\left){\begin{align}
  & 66 \\
 & \underline{63} \\
 & 03 \\
\end{align}}\right.}}\]
So we will get the remainder 3; i.e. $66\div 7=7\times 9+3$.
So we got the remainder 1, 2 and 3 for the number 64, 65, and 66 respectively. As now according to the question we had to sum up the remainder we get from these numbers when divided by 7; so the sum of remainders is equal to remainder of 64+remainder of 65+remainder of 66 when divided by 7. So we will get;
$\begin{align}
  & =1+2+3 \\
 & =6 \\
\end{align}$
Hence answer is 6.

Note: In this question we had to find the summation of remainder we get from the number 64, 65, and 65 after dividing it by 7; keep in mind that sum/summation means the addition of value.