Let me try this problem with 25 1's rather than 2004.
1111111111111111111111111 divided by 3
I did this, longhand and got
1111111111111111111111111 3 = 0370370370370370370370370
(I wrote the leading zero to help you see the pattern.) I count 9 zeros, but we usually don't count the leading zero, hence I would say that 1111111111111111111111111 divided by 3 has 8 zeros.
How can you tell there are 8 zeros without counting?
The pattern 037 is three digits long and and 11111111111111111111111111 is 25 digits long. 25 3 = 8 with a remainder of 1 so in the division, the pattern 037 repeats 8 times and then there is one more digit. Since the pattern starts with a zero there is one more zero. Thus there are 9 zeros, the same as we found by counting, but we don't count the leading zero.