I wouldn't call it a dual use word, just one with a range of connected meanings.
A bit like "draw" in English, perhaps - it can be used to mean "pull" (a horse-drawn cart; to draw one's sword) or to mean "make a picture" (draw a flower; a pencil drawing) - originally, I think, from the idea of "pulling your pencil across the paper".
Looks like it : http://geiriadur.ac.uk/gpc/gpc.html?rhannu (also "distribute")
Makes sense in a way since if you share your apples with your friends, you divide the apples into portions and then distribute the portions to the friends.
German also uses teilen for both "divide" and "share" (and austeilen or verteilen for "distribute").