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    • 2 Apr 2010

      100 Factorial

      Posted at 8:42 am by Admin, on April 2, 2010

      how many trailing zeroes are there in 100! (100 factorial)?

      Solution

      One per factor of 10, and one per factor of 5 (there are more than enough 2’s to pair with the 5’s), plus one per factor of ten squared (one occurrence) and one per factor of 5 squared (three occurrences).

      So if I’m counting correctly, that’d be 10 + 10 + 1 + 3== 24 zeroes.

      Assuming the question meant *trailing* zeroes. It’d be much harder to also count the intermingled zero digits in the entire expansion.

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