Dynamically create divs with incremented id using jquery

Your title and question content seem to disagree with each other. I am assuming you are wanting to create div's where each id sequentially increments each time one is created?

$(function(){
  var count = 0;
  $('#append').click(function(){
    $('#parent').append('<div id="first'+count+'">text</div>');
    count++;
  });
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<a id="append">Add DIV</a>
<div id="parent"></div>

You can change it with .attr():

$('#first').attr('id', 'first6')

try to change the code to :

<div id="first">text</div>
<div id="first0">text</div>
<div id="first1">text</div>
<div id="first2">text</div>
<div id="first3">text</div>
<div id="first4">text</div>
<div id="first5">text</div>

dont forget the id inside " " (id="first" not id=first)

now you can simply use jquery : $("#first").attr('id','first6');