Let $n = {p\_1}^{a\_1} \dots {p\_k}^{a\_k}$. Prove that $p\_1 \le \sqrt n$.

It seems intuitive, but is there a formal proof to this?

Context:

[![enter image description here](https://i.stack.imgur.com/cKf0W.png)](https://i.stack.imgur.com/cKf0W.png)