Hopefully this benefits someone, because it confused me until I read up: From what I understand, and don't take this as gospel, Zahl is used for stated numbers/figures. Like, "The NUMBER of provinces in Canada is 10."; whereas Anzahl is unstated numbers, like "Canada has a NUMBER of provinces."; whereas Nummer is an assigned number, like a telefonnummer (phone) or a hausnummer (address).
After googling it http://forum.wordreference.com/showthread.php?t=1206849 A more correct translation of Zahl seems to be "digit", цифра