Question

Is 10824 divisible by 11?

Answer 1

Hint: We first find the divisibility rule of 11. We find the difference of the summation of odd and even placed numbers. We also verify the result with the actual division and find the quotient.

Complete step by step solution:
We follow the divisibility rule of 11 to find the solution.
We can also use the divisibility rule of 11 where if the difference of the sum of odd and even placed numbers is divisible by 11 then the main number is divisible by 11.
In 10824, we find the even number placed digits as 2 and 0 and the addition gives $2+0=2$.
In 10824, we find the odd number placed digits as 1, 8 and 4 and the addition gives $1+8+4=13$.
The difference gives $13-2=11$ which is divisible by 11.
Therefore, 10824 is divisible by 11.

Note: We now complete the actual division to also show that 10824 divisible by 11.
We find the quotient value as an integer.
$11\overset{984}{\overline{\left){\begin{align}
  & 10824 \\
 & \underline{99} \\
 & 92 \\
 & \underline{88} \\
 & 44 \\
 & \underline{44} \\
 & 0 \\
\end{align}}\right.}}$
Since the remainder is zero we can say that 10824 is completely divisible by 11.