Question

When a natural number is divided by 10 what is the sum of all possible remainders?

Answer 1

Hint: Here the given question needs the sum of the possible remainders that can be achieved after a natural number is divided by ten, to get the answer we first need to see the possible remainders and then add them all to get the desired value.

Complete step by step answer:
Here the given question needs to check the possible remainders that can come if an natural number is divided by ten, and then need the sum of all those numbers, here lets see the possible remainders first, on solving we get:
Here we know that when a natural number will be divided by ten then it will give the remainder in unit place as \[0,1,2,3,4,5,6,7,8,9\] ,except unit place all places will be divisible by ten.
So here the sum of the remainders will be:
\[ \Rightarrow 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45\]
Here we get the answer for the question.

Note: Here in the given question we need to see the divisible rule, as we know that any natural when divided by ten will give remainder for unit place only if possible, rest will be completely divisible, so the possibilities of the remainder at unit place needed to be obtained here and then on getting the sum of all that possibility we had our answer.