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?


2 Answers 2


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:


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.

  • $\begingroup$ I think that's what I don't quite understand. What is this "multiply and substract" part about exactly? $\endgroup$
    – Saturn
    Mar 20, 2012 at 5:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.