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

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

• Why do you need a theorem? This can be simply proved using properties of inequality. Dec 15 '16 at 19:55
• The same theorem which says that $N$ can not have a proper divisor $\lt 2$.
– dxiv
Dec 15 '16 at 20:03

Suppose $M > N/2$. Then $2M > N$.
Thus, $M$ doesn't divide evenly into $N$ Because there is no number $a$ such that $aM = N$.
Proposition: there are no integers $n$ such that $$1 < n < 2$$