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 @lookup;
my %hash;

NLIST:
foreach my $num (@nlist) {
   foreach (@lookup) {
      my ($factor, $key) = @$_;
      if ($num % $factor == 0) {
         push(@{$hash{$key}}, $num);
         next NLIST;
      }
   }

   my $key = shift(@key_list);
   push(@lookup, [$num, $key]);
   $hash{$key} = [ $num ];
}

require Data::Dumper;
print(Data::Dumper::Dumper(\%hash));

##</code><code>##

$VAR1 = {
          'A' => [3,24,9,24,15],
          'B' => [8,16,8,16,8],
          'C' => [17,17],
          'D' => [23],
          'E' => [14,14,14],
          'F' => [25],
          'G' => [11,22],
          'H' => [19]
        };