I have 1x2x3x4x5x....x1000 = X ...So how many zero that X may have ?

Question

For example:
100 has 2 zero ;
1000 has 3 zero

Answer 1

well, basically all you want to do is count the number of 5s in it, because there are obviously more 2s, and 2*5 = 10. :)

5^1: 1000/5 = 200
5^2: 1000/25 = 40
5^3: 1000/125 = 8
5^4: 1000/625 = 1 (you round down)

Therefore there would be 200+40+8+1 = 249 zeroes.

Daniel: I didn't overcount numbers. There are 2 5's in 25, 50, etc. so I counted those numbers twice.

Answer 2

For each of 10, 20, 30, 40, 50, .. 970, 980, 990, 1000 add one zero....100.
For each of 100, 200, 900, 1000 add another...110.
For 1000, one more..........111.
There's 100 numbers ending in 5 and 100 numbers ending in 2............211.

I get 211 zeros (on the right). There may be other zeros on the left of a non-zero digit.

Bob's answer double counts the numbers....the number 5 is already counted in the 25.