How many factors of the number 684 are perfect squares?


  • M0★ M1 M2 M3

    Hi,

    In the placement test of Module 0 question 3, how many factors of the number 684 are perfect squares? We worked out that 684 = 2^2 x 3^2 x 19

    We knew that 2^2=4, 3^2=9, 2^2 x 3^2=6^2=36, please advise how to work out the other 3 perfect squares. Thanks!


  • ADMIN M0★ M1 M5

    @EW I apologize for this long delay to your question; we've been backed up a bit with the recent work on NOVID. 🙂 Thanks for asking! There's a neat trick to solving this that you will see in Module 0, which avoids having to list exactly what the squares are. I think you might have accidentally switched the digits in the number, because you found the prime factorization of \(684\), when it's actually supposed to be \(648.\) No problem! You look like you are on the right track.

    Happy Learning!

    The Daily Challenge Team


  • M0★ M1 M2 M3

    Thanks for your reply! Please correct the typo mistake in the placement test then as it is 684!


  • ADMIN M0★ M1 M5

    @EW Oops, you are totally right. That error slipped past our eyes. I've just fixed this; thanks so much for your patience and for letting us know right away! 🙂


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