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Math Help - Factorial

  1. #1
    Junior Member
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    Bogota D.D
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    Factorial

    Hi everyone.

    Show that if n is a integer, then is impossible that n! finish with 153, 154 or 155 zeros.

    Thanks so much.
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  2. #2
    Senior Member
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    Re: Factorial

    20! has 4 zeros because it has factors including 5,10,15 and 20. That gives us the factor 5 four times. There will always be enough 2s to pair up with the 5s.

    25! has 6 zeros because you have factors 5, 10, 15, 20 and 25. That gives us the factor 5 six times.

    Another example: 600! has 5,10,15....600 and 25,50,75...600 and 125,250,375,500. So how many zeros?

    600/5=120
    600/25=24
    int(600/125)=4
    I think that gives you 148 zeros.

    The answer lies near here.
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