Here's a recursive solution to find the closest set of factors to a target (with wrapper script). I think it's solid. 
use strict; 
use warnings;
use List::Util qw[ reduce ];

my @pfs = ( 2,3,3,3,7, 997 );
my $num = reduce { $a * $b } @pfs;
my $root = sqrt $num;
print "N=$num, R=$root\n";

sub closest {
  # Args are target and factor-list
  my ($target, $car, @cdr) = @_;
  @cdr or return $car;
  reduce { abs($target - $a) < abs($target - $b) ? $a : $b }
         ($car*closest($target/$car, @cdr), closest($target, @cdr), $c
+ar);
}

print closest($root, @pfs), "\n";

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Caution: Contents may have been coded under pressure.

In reply to Re^6: OT: Finding Factor Closest To Square Root by Roy Johnson
in thread OT: Finding Factor Closest To Square Root by QM

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