1. The problem statement, all variables and given/known data Prove that for a finite group A, the order of any element in A divides the order of A. 2. Relevant equations The order of an element a of a group A is the smallest positive interger n such that an = 1. 3. The attempt at a solution Well, I know that the order of a finite group A is the number of elements in A. I realize that the statement can be written as "if group A is finite, then the order of an element in A divides the order of A, which is set up nicely for a direct proof. Divisibility would entail that there exist some integer q such that for all elements of A, ord(a)q = ord(A). However, at this point, I don't have an idea as to how to carry out the proof. Any help would be greatly appreciated!