$\require{enclose}\enclose{horizontalstrike}{\rm Greatest}\!$ Least prime factor of $n$ is less than square root of $n$, proof I remember reading this somewhere but I cannot locate the proof.

It is the **smallest** prime factor that is less than or equal to $\sqrt{n}$, unless $n$ is prime. One proof is as follows: Suppose $n=ab$ and $a$ is the smallest prime factor of $n$, and $n$ is not prime. Since $n$ is not prime, we have $b\
e1$. Since $a$ is the smallest prime factor of $n$, we have $a\le b$. If $a$ were bigger than $\sqrt{n}$, then $b$ would also be bigger than $\sqrt{n}$, so $ab$ would be bigger than $\sqrt{n}\cdot\sqrt{n}$. But $ab=n$.