Factors and RectanglesDate: 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/ |
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