Remainder

Have you ever though about remainders?. Nothing great in it but thought of sharing it.
Its about Negative number division.
What is 14/3 ? Its 4.667. with 4 as quotient and 2 remainder. Hence 14/3=4 plus 2/3.
Now what is -14/3 or 14/-3? It should be -4.667, but some interesting facts.
What could be the quotient for (-14/3) ... -4 ? and remainder...... -1.. ?
I don't think so.

If we go to the basics, If the number which is not completely divisible by divisor we get a greatest integer number which is completely divisible by divisor but lesser that dividend and subtract it from dividend. The subtraction in nothing but the remainder. In above example if the quotient is -4 then -12 should be lesser that -14. But Its NOT. Also the remainder of the division can not be negative. It is the one which 'remains' (negative can not remain....huhhhh..!!)

So... continuing with the same example, what if quotient is -5..? Lets see.
3*-5= -15 , which is less that -14. And remainder is 1...Hurrrrrayyyyyy...!
So -14/3 = -5 plus 1/3 which turns to -4.667
Also for 14/(-3), quotient is -4 and remainder is 2
Hence 14/(-3) = -4 remainder 2 = -4 plus 2/(-3) = -4.667

This is called is Aditya's theory of remainder..... :)))))) (Good Joke)