Posted by sarah on Monday, July 20, 2009 at 12:07pm.
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.
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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