For the definition that follows, I'm curious to know if there's a known name (to enable a literature search relating to algorithms).
Definition. Given an integer $n$, the maximally square factorization consists of the integers $\{a,b\}$ such that $n=ab$ and the difference $|a-b|$ is minimized. Formally:
$\{a,b\} = \arg \min_{\{x,y : x|n, y|n, xy=n\}} |x-y|.$
Examples:
For $n=16$, we get $\{a,b\}=\{4,4\}$.
For $n=1300$, we get $\{a,b\}=\{26,50\}$.
Questions:
1) Does this concept have a name? Any closely related concepts are also of interest. Number theory is not my strength.
2) Is there some clever way for finding $\{a,b\}$ that doesn't require fully factorizing $n$ and taking the two integers closest to $\sqrt{n}$?