Largest Prime Factor - Implementation

Here is the full solution:

function largestPrimeFactor(n)
    largestFactor := 1
    i := 2
    while i * i <= n
        while n mod i = 0
            largestFactor := i
            n := n / i
        i := i + 1
    if n > 1 then
        largestFactor := n
    return largestFactor

Time: $O(\sqrt{n})$. Space: $O(1)$. The inner while loop divides out all occurrences of each prime factor before moving to the next.