You show more keys than numbers. This only warns if there are not enough keys.

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'..'D');

my ($result, @ans, $i) ;

for my $num ( @nlist ) {
    $i = 0;
    while ( 1 ) {
        if ( ! defined @{$ans[$i]}  or  0 == $num % ${$ans[$i]}[0] ){
            push @{$ans[$i]}, $num;
            last;
        }
        ++$i;
    }
}

$result->{ shift @key_list } = $_ for  @ans ;
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Be well,
rir