SOLUTION: Determine how many zeros are at the end of the numeral for the following in base 10: 1000! Please explain how we can find the number of zeros for any factorial.

Question 248731: Determine how many zeros are at the end of the numeral for the following in base 10:
1000!
Please explain how we can find the number of zeros for any factorial.
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
number of zeros = number of factors of 10 = number of factors of 5 (Factors of 5 are less common than factors of 2.)

Keep dividing the result by 5 until you can't.

1000/5 = 200
200/5 = 40
40/5 = 8
8/5 = 1.6 --> 1

1000! ends with 200 + 40 + 8 + 1 = 249 zeros.
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