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albert o
albert o asked in Science & MathematicsMathematics · 1 decade ago

why all numbers of the form ABABAB are divisible by 7?

3 Answers

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  • Mugen is Strong
    Lv 7
    1 decade ago
    Favorite Answer

    because ABABABs are products of AB and 10101, where 10101 are multiple of 7.

  • Northstar
    Lv 7
    1 decade ago

    Split the number into two pieces and check to see if they are divisible by 7.

    ABABAB = (10000B + 100B + B) + (100000A + 1000A + 10A)

    ABABAB = 10101B + 101010A

    But 10101 / 7 = 1443

    So we have:

    10101B + 101010A = 1443B + 14430A which is an integer

    So all numbers of the form ABABAB are evenly divisible by 7.

  • kkr
    1 decade ago

    An example of 'number form' stated by you is...

    131313, which is technically 13*(010101)

    All numbers like this has said common factor '010101'

    As 10101/7 is 7* 1443, said 7 is a factor of all numbers of the form ABABAB!

    Regards.

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