Question

What least number should be added to 1056, so that the sum is completely divisible by 23?

Answer 1

Hint: Use the basic concept of Remainder and quotient i.e. \[Dividend{\text{ }} = {\text{ }}Quotient \times Divisor\; + \;Remainder\].

Complete step-by-step answer:

We know that, \[Dividend{\text{ }} = {\text{ }}Quotient \times Divisor\; + \;Remainder\] (equation 1)

On replacing values given in the question in equation 1 we get
When we divide 1056 with 23, we get 21 as a remainder.
So, 23−21=2
So, 2 must be added to 1056 in order to make the sum completely divisible by 23.
∴ 1056+2=1058

Now, we can see that when 1058 is divided by 23 we get 46 as quotient and 0 as remainder.
∴ The least number that should be added to 1056, so that the sum is completely divisible by 23 is 2.

Note: In these types of questions always remember the basic formulas. As you can see the above question is completely formula based and just replacing the values of Dividend, Divisor, and quotient gives you the remainder and leads you to the solution.