Question

On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?

Answer 1

Hint: In the question it is given that on dividing a number by 56 we get the remainder as 29. We are asked that on dividing the same number with 8 what will be the remainder. So here we use the concept of division that\[divisor=dividend\times quotient+remainder\]. Here we proceed further using the given values dividend is 56 and the remainder is 29.

Complete step by step answer:
Firstly, from the given it is known that dividend is 56 and remainder as 29.
So let us consider the quotient as x and proceed further by using the above mentioned property. So the equation will be reduced as follows.
\[\Rightarrow divisor=dividend\times quotient+remainder\]
By substituting the values in the above property we will get the equation as follows.
\[\Rightarrow number=56\times x+29\]
Since the number gives 29 as remainder on dividing by 56, we can write the above equation.
After some simplification the equation will be as follows.
\[\Rightarrow number=7\times 8\times x+3\times 8+5\]
In the question it is asked that on dividing the same number with 8 what will be the remainder. So by simplifying the number and by observing it in its simplified form
We can get the required solutions as follows.
\[\Rightarrow number=7\times 8\times x+3\times 8+5\]
\[\Rightarrow number=\left( 7\times x+3 \right)\times 8+5\]
Here from observing the equation we can say that the number is divisible by 8 and the remainder when divided will be 5.

So the required solution will be 5.

Note: We must be very careful in knowing the concept of the division property and the person must be careful in division of numbers.
These kind of division problems can also solved in other ways for example the same question can be solved in another method as
\[\Rightarrow number=56x+29\] let the x as 1 so the equation will become as \[\Rightarrow number=56+29\] \[\Rightarrow number=85\] so here when the number is divided with 8 the remainder will be 5.