# Standard way to divide numbers of base other than 10.

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?

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 $7$.

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.

• I think that's what I don't quite understand. What is this "multiply and substract" part about exactly? – Zol Tun Kul Mar 20 '12 at 5:08