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Cake day: August 15th, 2023

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  • 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.