Thanks for the detailed explanation!

Sometimes i get very sloppy when I write. My apologies, i should not have used the word factorize instead i should have used the word 'cancel' out.. Actually I was thinking more in terms removing'like' elements. This is in reference to your code.

In the code that I had, I was removing further cancelable terms

Going back to your example

{ multiply and divide remaining terms }

5 * 6 * 7
---------
  2 * 3

The program I had would have done this before multiplying

5 * 7
-----
  1
{result}
  35
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n!/k! = PI(x) where x goes from (k+1) to (n) assuming n > k; PI(x) sta
+nds for product of<p>
<readmore>
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#!/usr/bin/perl

use strict;
use warnings;

# Numerator and Denominator specified as factorials [BrowserUk]'s exam
+ple numbers

my @snum = (44_289, 11_800, 10_389, 4570);
my @sden = (56_089, 989, 9_400, 43_300, 2_400);

# old list from previous node
# my @snum = (44_289, 11_800, 10_389, 45_700);
# my @sden = (56_089, 989, 9_400, 43_300, 11_800, 2_400);
#
@snum = sort {$b<=>$a} @snum;
@sden = sort {$b<=>$a} @sden;

my $i = 0;

# Make the arrays equal size
if (@snum < @sden) {
    foreach $i (@snum..$#sden) { $snum[$i] = 0;}
} else {
    foreach $i (@sden..$#snum) { $sden[$i] = 0;}
}

print +($_,$/) for (@snum);
print $/;
print +($_,$/) for (@sden);
print $/;

my @nexp = ();
my @dexp = ();

# n!/k! = (k+1)..(n) [assuming n > k]
for $i (0..$#snum) {
    if ($snum[$i] > $sden[$i]) {
        print ("Numerator: Going to push from ", $sden[$i]+1, " to ", 
+$snum[$i],$/);
        push (@nexp, (($sden[$i]+1)..$snum[$i]));
    } elsif ($sden[$i] > $snum[$i]) {
        print ("Denominator: Going to push from ", $snum[$i]+1, " to "
+, $sden[$i],$/);
        push (@dexp, (($snum[$i]+1)..$sden[$i]));
    }
}

print ("Length of expanded numerator   = ", scalar @nexp, $/);
print ("Length of expanded denominator = ", scalar @dexp, $/);
print ("Total Number of elements = ", scalar @nexp + scalar @dexp, $/)
+;
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