Classically, a "division" is about 10,000. In most armies, it is pretty safe to figure out about that many. For our military, it is reasonable also, but the type of division is pertinent to know - infantry, armored, etc. If you know the type of division in the US, you can get a real good idea. I believe an Iraqi "division" was scheduled to be a fair bit larger than 10,000.
"Element of a division" is just some part of it - it could be only a couple hundred or nearly the whole division.
Given the massive attrition which has been inflicted on these Iraqi forces, I suspect that there are far less than 10,000 around the airport. One of the major divisions was essentially deployed in that area, though, and may be fairly intact.