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I would like to know why this division 2/16 has a remainder of 2.

I understand remainders from this division 10/6 = 1 remainder is 4.

But I can't figure out why 2/16 has a remainder of 2.

Thanks

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closed as off-topic by Xander Henderson, user175968, cmk, metamorphy, José Carlos Santos Jul 23 at 19:01

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  • 3
    $\begingroup$ $2 = 0\cdot 16 + 2$. $\endgroup$ – Randall Jul 22 at 17:47
  • $\begingroup$ or $2\div16="0$ with remainder $2"$ $\endgroup$ – J. W. Tanner Jul 22 at 17:48
  • $\begingroup$ What would you expect the remainder to be? $\endgroup$ – Alexander Jul 23 at 3:30
  • $\begingroup$ Why was this question closed? It certainly provides context. $\endgroup$ – Matt Samuel Jul 26 at 16:55
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$16$ goes into $2$ a total of $0$ times. Therefore the quotient is $0$ and the remainder is $2$. This happens whenever the dividend is smaller than the divisor.

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$2/16 = 0 .... 2$

In other words,

$2 = 16 * 0 +2$

Intuitively, doing this division asks you to make choice of a largest number, which, after being multiplied by the divisor (in this case, 16) must not exceed the number being divided (in this case, 2); (so this choice has to be $0$ other wise you exceed $2$). Now whatever remains is the remainder (in this case, 2).

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If $a < b$, then $a \mod b = a$. In particular, $2 \mod 16 = 2$.

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You can say that $2/16$ has a remainder of 2 because $2=16.0+2$ which is essentially the remainder.

It would also be correct to say that it has a remainder of $-14$ (I know that this is strange but it is true and this fact is helpful to know for some questions, although not of much help for this one) and in fact this is used in some proofs of modular arithmetic in number theory. Just a side fact!

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