Why
6 % 10 = 6
As fa as I know 10 % 6 = 4, but I don't know how to handle the first one
Thanks!
$\endgroup$ 42 Answers
$\begingroup$The modulo operator a mod b gives the remainder when you divide a by b. Can you then work out the remainder when 6 is divided by 10?
$\endgroup$ 2 $\begingroup$Division Theorem:
For any integer $M$ and any natural $n$ then if you divide $N$ by $n$ you will get a unique integer quotient $q$ and unique remainder integer $r$, between $0$ (inclusive) but less than $n$ so that $M= qn + r$.
$r$ is the remainder and $0 \le r < n$ and $q$ is the quotient and $q \le \frac Mn < q+1$.
And $M\% n = r$. That is the definition.
SO if $M = 6$ and $n = 10$ what are $q$ and $r$ so that that:
$6 = q*10 +r$ and $q \le \frac{6}{1} < q+1$?
THe answers are:
$q=0$ and $r =6$.
$6 = 0*10 + 6$.
And so $6\% 10 =6$
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