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Factorial Frenzy

Source: 2006 AIME A Problem 4

March 9, 2006
factorialnumber theoryprime factorizationAMC

Problem Statement

Let NN be the number of consecutive 0's at the right end of the decimal representation of the product 1!×2!×3!×4!⋯99!×100!.1!\times2!\times3!\times4!\cdots99!\times100!. Find the remainder when NN is divided by 1000.
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