Jquery later allowed you to to find the parents with the .parents()
method.
Hence I recommend using:
var $div = $('#divid').parents('div[class^="div-a"]');
This gives all parent nodes matching the selector. To get the first parent matching the selector use:
var $div = $('#divid').parents('div[class^="div-a"]').eq(0);
For other such DOM traversal queries, check out the documentation on traversing the DOM.