Largest Prime Factor - Algorithm

Here is the algorithm:

$1.$ Initialize $largestFactor = 1$ and $i = 2$.

$2.$ While $i \times i \leq n$: if $i$ divides $n$, set $largestFactor = i$ and divide $n$ by $i$. Otherwise, increment $i$.

$3.$ If $n > 1$ after the loop, then $n$ itself is the largest prime factor.

$4.$ Return $\max(largestFactor, n)$.