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Math Help - what is the remainder when

  1. #1
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    what is the remainder when

    1!+2!+3!+4!+.....+100! is devided by 15 ? and how to calculate it ?
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  2. #2
    Moo
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    Hello,

    You can notice that 15=3x5

    This means that for all n > (or equal) 5, n! will contain 15 in its factors.

    So we know that (5!+6!+...+100!) is a multiple of 15.

    1!+2!+3!+4!=1+2+6+24=33

    --> the remainder is 3.
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