Math CentralQuandaries & Queries


Question from Nnubia:

1021 in base 3 divided by 2 in base 3

Hi Nnubia,

I responded to a similar question a while ago using base 7. I suggest you look at my response. In the question the original numbers were given in base 10 so it was necessary to convert to base 7 before starting the division. For base 3 let me look at dividing $120_3$ by $2_3 .$

The firs step is to construct a multiplication table of the divisor $2_3 .$ This is particularly easy in base 3 since there are only 3 digits, $0_3 ,1_3$ and $2_3 .$ thus the table is

$0_3 \times 2_3 = 0_3$

$1_3 \times 2_3 = 2_3$

$2_2 \times 2_3 = 11_3$

Now try to use the technique I used in the base 7 example to calculate $120_3$ divided by $2_3 .$ I got $21_3$ with a remainder of 1. Now try your problem and write back if you need more assistance.


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