Please let me know why 2/16 has a remainder of 2. Thanks

Question

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

Answer 1

$16$ 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.

Answer 2

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

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).

Answer 3

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

Answer 4

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!