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I have question on behavior of floor division. if i have,

-7/3 = -3 and remainder = 2
also -7/3 = -4 remainder = 5   

it can have many results. When we make tally all are correct.Then what is the use of floor division is not stick to one solution as truncated division.
Where floor division can be applied any example.

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It means $5\equiv 2\pmod 3$... in this case, we pick the least positive remainder. – J. M. Jul 22 '12 at 9:40
up vote 1 down vote accepted

The Division Theorem says that if $a$ and $b$ are integers, $b\ne0$, then there are unique integers $q$ and $r$ such that $$a=bq+r,\quad0\le r\lt|b|$$ So there is only one result, with that condition on the remainder, $r$.

The Division Theorem is the first step in the most frequently seen proof of the Unique Factorization Theorem. Generalizations of the Division Theorem can be used to prove uniqueness of factorization in many other settings, for example, unique factorization of polynomials with real coefficients.

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Thanks Gerry Myerson. – sandip karanjekar Jul 22 '12 at 9:59

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