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Math Help - find the perfect squres!

  1. #1
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    find the perfect squres!

    Compute the number of perfect squares that are factors of (5!+6!+7!)^3
    Last edited by mr fantastic; February 25th 2010 at 01:46 AM. Reason: Edited post title.
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  2. #2
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    Quote Originally Posted by victorlui View Post
    Compute the number of perfect squares that are factors of (5!+6!+7!)^3
    This is easy. Just find the number, take the square root of it, and try dividing all perfect squares smaller than that into the original total
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  3. #3
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    All positive integers up to 5 are factors of 5! and so factors of 6! and 7! as well. Since the expression is cubed, each of those, squared, will be a perfect square dividing the expression. Also, both 2 and 3 are in 5! so 6 is a factor of 5!, 6!, and 7!. 6^2 is also a perfect square dividing the expression.
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