Finding the id of a parent div using Jquery

I have some html like this:

<div id="1">
    <p>
        Volume = <input type="text" />
        <button rel="3.93e-6" class="1" type="button">Check answer</button>
    </p>
    <div></div>
</div>

and some JS like this:

$("button").click(function () {
    var buttonNo = $(this).attr('class');
    var correct = Number($(this).attr('rel'));

    validate (Number($("#"+buttonNo+" input").val()),correct);
    $("#"+buttonNo+" div").html(feedback);
});

What I'd really like is if I didn't have to have the class="1" on the button (I know numeric classes aren't valid, but this is a WIP!), so I could determine buttonNo based on the id of the parent div. In real life there are multiple sections looking like this.

1. How do I find the id of the div parenting the button.

2. What would be a more semantic way to store the answer in the button code. I want to make this as foolproof as possible for a non programmer to copy and paste without breaking things!