If I had been taught to do division this way in my own schooling, I don't think that I would dislike it as much as I do. You can also set up the problem as sixteen minus 4, and keep subtracting four until you get zero:
16
-4
12
-4
8
-4
4
-4
0
One you get to zero, you go back and count how many times you took away four, which is four times, and you've got your answer: 16/4=4.
This method works wonderfully with all types of division problems, and greatly decreases frustration and confusion that the method of long hand division creates. The example below is a division problem that does not divide evenly:
55/6=?
55
-6
49
-6
43
-6
37
-6
31
-6
25
-6
19
-6
13
-6
7
-6
1
For this problem, you cannot get down to zero because 6 does not go into 55 evenly, you are left with a remainder of 1. Now that you know your remainder, you go back through and count how many times you subtracted 6, which is 9 times. Thus your final answer to 55/6=9R1.
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