Div. is the written short form of division. You see it on paper, in names, and in lists — people do not usually say “div.” out loud. You have to read the context, because division is several different kinds of grouping. In a company, the Sales Div. is a department. In the army, a Div. is a large group of soldiers. In sport it can mean a league group (First Div.). In a school or exam paper it can mean a grouping of students or results. Though actually the same three letters can stand for other words in other fields (and spoken “div” is a different, slangy thing), this entry is the abbreviation of division. The full word is what you say. A period after Div is common in older and British-style writing.