Which theorem states that a number N can't be perfectly divided by a number greater that N/2 ?

Question

Which theorem states that a number N can't be perfectly divided by a number greater that N/2?

Answer 1

Just think about it:

Suppose $M > N/2$. Then $2M > N$.

Thus, $M$ doesn't divide evenly into $N$ Because there is no number $a$ such that $aM = N$.

Answer 2

Proposition: there are no integers $n$ such that $$ 1 < n < 2 $$