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Determining Number of Consecutive Zeros

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How many consecutive 0's are there at the end of the number (50!)^3 ("50 factorial" cubed)?

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Solution Summary

This solution discusses the theory behind the determination of the number of consecutive 0's at the end of a positive integer is reviewed, and is then applied to this particular problem. A complete, detailed solution is provided.

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First, note that for any positive integer n, the number of consecutive 0's at the end of n^3 is three times the number of consecutive 0's at the end of n itself. Thus we first determine the number of consecutive 0's at the end of 50! (and then multiply that number by 3).

Every 0 at the end of a positive integer stems from a factor of 10, which in turn stems from a ...

Solution provided by:
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
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