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Convert the base-ten number to a numeral in the indicated base.
329 to base six

  • math -

    Find the greatest power of 6 that is less than or equal to 329.

    6^0 = 1
    6^1 = 6
    6^2 = 36
    6^3 = 216
    6^4 = 1296

    So you need to start with 6^3.

    Divide 329 by 216, then take the remainder and go to the next lowest power.

    329 / 216 = 1 R 113

    Now divide 113 by 6^2

    113 / 36 = 3 R 5

    Now divide 5 by 6^1

    5 / 6 = 0 R 5

    Now divide 5 by 6^0

    5 / 1 = 5 R 0

    Using the quotients, the number in base 6 is 1305.

  • math -

    You can also do this the other way around. Compute the last digit by taking the remainder after division by 6:

    329 mod 6 = 5

    Subtract 5 and divide by 6 to obtain:

    (329 - 5)/6 = 54

    Then the first digit of 54 in base 6 will be the next digit. So, we can just iterate the process with 329 replaced by 54:

    54 mod 6 = 0 : next digit is 0

    54/6 = 9

    9 Mod 6 = 3 : next digit is 3

    (9 - 3)/6 = 1 which is simply 1 in base 6, so the last digit is 1.

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