It's quite straight forward:
function openPopup(idDiv)
{
$('#'+idDiv).dialog();
}
And you pass the function on each button respectively:
<input type="button" önclick="openPopup('div1')" value="btn1" />
<input type="button" onclick="openPopup('div2')" value="btn2" />
<input type="button" onclick="openPopup('div3')" value="btn3" />
Edit:[Nirav Prabtani]
Set
$('#'+idDiv).dialog();
instead
$
('#idDiv').dialog();