Proving that a composite number $n$ has a factor $k \leq \sqrt{n}$ 
Prove that a composite number $n$ has a factor $k \leq \sqrt{n}$.

Do we prove by proof by contrapositive?

Prove that a prime number $n$ has no factor $k \leq \sqrt{n}$.

Any tip?

If $n$ is composite, then $n=ab$ for some integers $a,b>1$. If $a,b > \sqrt{n}$, then $n=ab>\sqrt{n}\sqrt{n}=n$, a contradiction.
Note that the contrapositive of saying that a composite has such a factor is that if there is no such factor then it is not composite, not that a prime has no such factor.
