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Math Help - help please, number of factors

  1. #1
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    help please, number of factors

    wat is the highest # that n can be if 90!/2^n is a whole #
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  2. #2
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    How many even factors are there in 90!?
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  3. #3
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    45?
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  4. #4
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    It is given by
    [\frac{90}{2}] + [\frac{90}{4}] + [\frac{90}{8}] + [\frac{90}{16}] + [\frac{90}{32}] + [\frac{90}{64}] + [\frac{90}{128}] +.......
    That is, 45+22+11+5+2+1+0+..... = 86
    so n=86
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  5. #5
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    i still dont get it how did u get that equation, and 90/4 is 22.5, and 90/8 is 11.25.
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  6. #6
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    Quote Originally Posted by xinzhuang53 View Post
    i still dont get it how did u get that equation, and 90/4 is 22.5, and 90/8 is 11.25.
    That is not simple division. It is the floor function or the greatest integer function.
    \left\lfloor {\frac{{90}}{8}} \right\rfloor  = 11
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  7. #7
    Lord of certain Rings
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    Quote Originally Posted by xinzhuang53 View Post
    i still dont get it how did u get that equation, and 90/4 is 22.5, and 90/8 is 11.25.
    [] stand for floor function.

    The equation comes from counting all even numbers in 90! that is [\frac{90}2]
    Then counting all multiples of 4 that give an additional multiple of 2 in 90!, that is [\frac{90}4]
    Then counting all multiples of 8 that give yet another additional multiple of 2 in 90!, that is [\frac{90}8]
    And so on....
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