Associated Topics || Dr. Math Home || Search Dr. Math

### Small Base, Long Division

```Date: 10/06/2015 at 10:58:44
From: obinna
Subject: with respect to division of numbers with bases other than te

How can I divide 12343 by 24 in base five?

I haven't tried it, it's just too confusing.

```

```
Date: 10/06/2015 at 21:31:06
From: Doctor Peterson
Subject: Re: with respect to division of numbers with bases other than te

Hi, Obinna.

Here is an example of division in base five using different numbers, so
you can practice with your own:

Divide 2431 by 32 in base five.

First, I'll do something my son did when he was learning to divide, and
which is very helpful in other bases: make a list of multiples of the
divisor, to make it easy to find the appropriate quotient. This requires
only repeatedly adding the divisor, all work being in base five.

32   32*1
+ 32
----
114   32*2
+ 32
----
201   32*3
+ 32
----
233   32*4
+ 32
----
320   32*10

(I didn't need that last addition, but did it as a check: the answer is
clearly right, so I probably did all the additions in between correctly.)

The resulting multiplication table is

1    2    3    4
+-----------------
32 |32  114  201  233

Now I can start the division:

4
-------
32 ) 2431    <-- The biggest multiple less than 243 is
233     <-- 233, which is 4*32, so the quotient is 4.
---
10     <-- Subtract 233 from 243, leaving 10

Now I "bring down" the next digit, 1, and repeat the process:

41
-------
32 ) 2431
233
---
101    <-- The biggest multiple less than 101 is
32    <-- 32, which is 1*32, so the quotient is 1.
---
14    <-- Subtract 32 from 101, leaving 14

The quotient is 41 base five, and the remainder is 14 base five.

To check the answer, we can convert to base ten.

Our answer is a claim that

32 * 41 + 14 = 2431 (base five)

Converting to base ten, this is

17 * 21 + 9 = 366 (base ten)

This is correct!

We could also check by multiplying in base five, if you prefer:

32
* 41
----
32
233
----
2412
+ 14
----
2431

Again, the check passes.

Now try your problem; if you have trouble, show me your work and I can

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Division