Treebeard's Stumper

Stumper 100!
After 3 1/2 years of writing stumpers for the Dunn Middle School Friday Newsnote, this is stumper number 100! Yahoo! "100!" is also a math expression pronounced "100 factorial". It means the product of all the whole numbers up to that number multiplied together. For example, 10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3,628,800. Note the two zeros at the end. 100! is a huge number, way too big for my calculator. But I know it ends with an even longer string of zeros. How many zeros are there at the end of 100 factorial? How about 1000!? (Hint: 10 = 2 x 5)
Answer
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