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6 June, 13:50

How many perfect squares divide the number 4!·5!·6!?

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  1. 6 June, 16:12
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    4! = 24

    The perfect square factors of 4! are 1 and 4.

    5! = 120

    The perfect square factors of 5! are 1 and 4.

    6! = 720

    The perfect square factors of 6! are 1, 4, 9, 16, 36, and 144.

    Those are the perfect square factors of the big product as well:

    1, 4, 9, 16, 36, and 144.
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