how to loop over the child divs of a div and get the ids of the child divs?

Try this

var childDivs = document.getElementById('test').getElementsByTagName('div');

for( i=0; i< childDivs.length; i++ )
{
 var childDiv = childDivs[i];
}

Here's the solution if somebody still looks for it

function getDivChildren(containerId, elementsId) {
    var div = document.getElementById(containerId),
        subDiv = div.getElementsByTagName('div'),
        myArray = [];

    for(var i = 0; i < subDiv.length; i++) {
        var elem = subDiv[i];
        if(elem.id.indexOf(elementsId) === 0) {
            myArray.push(elem.id);
        }
    }
    return myArray;
}
console.log(getDivChildren('test', 'test-'));

You can loop through inner divs using jQuery .each() function. The following example does this and for each inner div it gets the id attribute.

$('#test').find('div').each(function(){
    var innerDivId = $(this).attr('id');
});