Maybe others have had a different experience, but I have found that I might as well dig the entire clump and divide it(much easier) than try to pick fans from around it. Even though it seems you are not really disturbing the original clump it seems I do, maybe others have better luck with that. But when I try to just pick out a few fans (unless they are on the fringe or edges) it seems to set the plant back till the next season.
