Simply find the remainder

Number Theory Level 2

Find the remainder when -26 is divided by 5.

Clarification: The remainder is strictly non-negative.

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Does not exist 1 -1 4

5 solutions

Sandeep Bhardwaj
Dec 2, 2014

This is very simple but conceptual one : $Dividend=Divisor \times quotient+Remainder$ $-26=(-5) \times 6 +4$ On comparing, Remainder=4 .

NOTE :

Now the question arises that why we didn't write it as : $-26=(-5) \times 5 +(-1)$ . If we do it so, then on comparing remainder will come out to be $-1$ .

But always Remember one thing about remainder that $0 \leq Remainder <divisor$

So from here, we can also conclude the Remainder can never be negative.

Very nice problem indeed. I actually forgot $0\leq r<b$ because I'm used to using negative remainders for modulo

Marc Vince Casimiro - 6 years, 6 months ago

Using negative remainders to ease out calculations is a valid process, but yes, by definition of remainder, we cannot give negative values as a final answer.

Prasun Biswas - 6 years, 5 months ago