Question

What least number must be added to \[1056\] , so that the sum is completely divisible by \[23?\]
$
A.{\text{ }}2 \\
B.{\text{ }}3 \\
C.{\text{ }}18 \\
D.{\text{ }}21 \\
E.{\text{ None of these}} \\
$

Answer 1

Hint- For solving such a type of question, we will start by dividing 1056 by the given number 23. Find some number by manipulating the remainder with the divisor in order to get a completely divisible number.

Given that 1056 must be divided.
And the divisor is 23.
When we divide 1056 by 23 we get
$1056 = \left( {23 \times 45} \right) + 21$
Where, 21 is the remainder.
To find the smallest number to be added in the dividend.
Subtract the remainder from the quotient.

$ \Rightarrow 23 - 21 = 2$
So 2 must be added and the new dividend becomes
$ \Rightarrow 1056 + 2 = 1058$
Which is completely divisible by 23.
Hence, 2 is the least number to be added.
Option A is the right option.

Hint- In such types of questions where we need to find the minimum or maximum nearest divisible number, we must start with the number taken into consideration and further manipulate with the divisor and the remainder. If the question was to find the smallest number to be subtracted, we would directly subtract the remainder.