First of all, the answer you got manually was wrong. 'F' contains 25, not 16, all the 16's went to 'B' already.

use strict;
use Data::Dumper;


my @nlist = (3,24,8,17,23,14,17,9,16,24,25,11,22,14,14,8,19,16,15,8);

my @key_list = ('A'..'Z');

my $hoa;

my $key_index = -1;
while (@nlist) {
    $hoa->{$key_list[++$key_index]}[0] = splice(@nlist, 0, 1);
    my $i = 0;
    while ($i <= $#nlist) {
        if ($nlist[$i] % $hoa->{$key_list[$key_index]}[0]) {
            $i ++;
        } else {
            push @{$hoa->{$key_list[$key_index]}}, splice(@nlist, $i, 
+1);
        }
    }    
}

print Dumper $hoa ;
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