• m_f@midwest.social
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    3 hours ago

    ⅐ = 0.1̅4̅2̅8̅5̅7̅

    The above is 42857 * 7, but you also get interesting numbers for other subsets:

         7 * 7 =     49
        57 * 7 =    399
       857 * 7 =   5999
      2857 * 7 =  19999
     42857 * 7 = 299999
    142857 * 7 = 999999
    

    Related to cyclic numbers:

    142857 * 1 = 142857
    142857 * 2 = 285714
    142857 * 3 = 428571
    142857 * 4 = 571428
    142857 * 5 = 714285
    142857 * 6 = 857142
    142857 * 7 = 999999
    
  • TwilightKiddy@programming.dev
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    8 hours ago

    The divisability rule for 7 is that the difference of doubled last digit of a number and the remaining part of that number is divisible by 7.

    E.g. 299’999 → 29’999 - 18 = 29’981 → 2’998 - 2 = 2’996 → 299 - 12 = 287 → 28 - 14 = 14 → 14 mod 7 = 0.

    It’s a very nasty divisibility rule. The one for 13 works in the same way, but instead of multiplying by 2, you multiply by 4. There are actually a couple of well-known rules for that, but these are the easiest to remember IMO.

    • darkpanda@lemmy.ca
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      7 hours ago

      If all of the digits summed recursively reduce to a 9, then the number is divisible by 9 and also by 3.

      If the difference between the sums of alternating sets digits in a number is divisible by 11, then the number itself is divisible by 11.

      That’s all I can remember, but yay for math right?

      • TwilightKiddy@programming.dev
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        7 hours ago

        Well, on the side of easy ones there is “if the last digit is divisible by 2, whole number is divisible by 2”. Also works for 5. And if you take last 2 digits, it works for 4. And the legendary “if it ends with 0, it’s divisible by 10”.

  • OfficerBribe@lemm.ee
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    7 hours ago

    Never realized there are so many rules for divisibility. This post fits in this category:

    Forming an alternating sum of blocks of three from right to left gives a multiple of 7

    299,999 would be 999 - 299 = 700 which is divisible by 7. And if we simply swap grouped digits to 999,299, it is also divisible by 7 since 299 - 999 = -700.

    And as for 13:

    Form the alternating sum of blocks of three from right to left. The result must be divisible by 13

    So we have 999 - 999 + 299 = 299.

    You can continue with other rules so we can then take this

    Add 4 times the last digit to the rest. The result must be divisible by 13.

    So for 299 it’s 29 + 9 * 4 = 65 which divides by 13. Pretty cool.