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    54 mod 4

    Module 5 Day 1 Challenge Part 7
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    • B
      Bella M0 M1 M2 M3 M4 M5
      last edited by Bella

      Professor Loh told us 27 + 27 (mod 4) = 3 + 3, which equals 6. The calculator says 27 + 27 (mod 4) = 2. Why?

      pulleybearP 1 Reply Last reply Reply Quote 0
      • S
        studiouszebra M0★ M1
        last edited by

        See I don't have module 5 but I know some mod.
        27 mod 4 = 3:
        because
        27 = 6 * 4 + 3

        and
        54 = 13 * 4 + 2
        now
        54 = 27 + 27 = (6 * 4 + 3) + (6 * 4 + 3)
        54 = (6 * 4 ) + (6 * 4 ) + (3 + 3)
        54 = (6 * 4 ) + (6 * 4 ) + 4 + 2
        54 = 4( 12 + 1) + 2

        54 = 13 * 4 + 2
        And I don't know Professor said that but I thought this would work.
        Sorry if I misunderstood.

        1 Reply Last reply Reply Quote 1
        • pulleybearP
          pulleybear M0 M1 M2 M3 M4 M5 @Bella
          last edited by

          @Bella Both are actually correct. I believe Professor Loh first found 27 (mod 4) to be 3, and then doubled this to get 6. Professor Loh is emphasizing the simplification step, which makes working with larger numbers easier. And if we simplify this further, 6 is 2 (mod 4). So your calculator is not wrong; 27 + 27 is 2 (mod 4). But noting Professor Loh's strategy will help you solve these types of problems more efficiently 🙂

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