Standard way to divide numbers of base other than 10.

Question

I have some homework where I am supposed to divide two numbers that are base 5 or 3.

And I did it. I basically converted the numbers to decimal, divided, and then convert the result to the original base.

That seems to work. But also seems a bit silly when I look at it. The reason I did such conversions is because I am not very sure of the fastest, simplest way to actually do such divisions. So, what do you do?

Answer 1

You can also use the ordinary long division algorithm, provided that you know (or can quickly work out) the single-digit multiplication and subtraction tables for the base in which you’re working. To divide $12343_{\text{five}}$ by $24_{\text{five}}$, for instance:

                 234  
               -----  
            24)12343  
               103  
               ---  
                204  
                132  
                ---  
                 223  
                 211  
                 ---  
                  12

That is, the quotient is $234_{\text{five}}$, and the remainder is $12_{\text{five}}$. In base ten I’ve divided $973$ by $14$ to get a quotient of $69$ and a remainder of $7$.

Answer 2

You can also just operate in base 5 or 3. The division algorithm you learned doesn't depend upon the base. You just need to multiply and subtract in the base of interest. Base 5: 13 into 233: first digit is a 1, leaving 103. Next is 3, and 3*13=44 leaving 4, so 233/13=13 remainder 4.