Question

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

Answer 1

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.

Answer 2

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.