Doesn't use Math::Big::Factor, isn't particularly dynamic, doesn't have exponential complexity, and could be much faster in C. With all those caveats, here you go...

#!/usr/bin/perl -w
use strict;

print sqrt_factor(shift), "\n";

sub sqrt_factor 
{
    my $n = shift;
    my $root = int(sqrt($n));

    for (my $i=$root; $i>1; $i--)
    {
        if( ($n % $i) == 0 )
        {   
            my $factor2 = int($n / $i);
            return (($root - $i)<($factor2 - $root)) ? $i : $factor2
        }
    }
    
    return 1;
}
[download]