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### Factors and Rectangles

```
Date: 06/25/98 at 18:22:52
From: amy
Subject: Factors and rectangles

I'm trying to figure out what a rectangle and factors have in common.
```

```
Date: 06/26/98 at 12:48:50
From: Doctor Peterson
Subject: Re: Factors and rectangles

Hi, Amy -

The answer is pretty simple, but it can give you a lot to think about.

Since the area of a rectangle is the product of the lengths of the
sides, the sides are always factors of the area.

It's easier to picture if you think of building a rectangle out of
objects - maybe little square blocks, or maybe just arranging coins in
a rectangle. If I gave you a handful (or a roomful) of blocks and
asked you to make a rectangle out of them, you would have to decide
what size rectangle you should build. Not all rectangles would work.
For example, if you had 14 blocks and tried building a rectangle 5
blocks across, you would find that you didn't have enough to make the
third row:

O O O O O
O O O O O
O O O O

That's because 5 is not a factor of 14. If you factor 14, you will
find that 14 = 2 * 7, so the only rectangles you could make would be
2 by 7 or 7 by 2:

O O O O O O O    O O
O O O O O O O    O O
O O
O O
O O
O O
O O

Oops - I forgot you could also make a 1 by 14 or a 14 by 1 rectangle -
they're easy to forget!

The fun part comes when you have a number that can factor in more
ways. For example, with 36 blocks you could make all these rectangles:

1 * 36
2 * 18
3 * 12
4 *  9
6 *  6
9 *  4
12 *  3
18 *  2
36 *  1

Try playing with rectangles for a while. It can really help you get a
feel for how multiplication and factoring work!

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

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