Prime, Composite, or Neither?Date: 09/16/2003 at 19:02:12 From: Hillary Subject: prime and composite numbers What are prime and composite numbers? I just don't get it. Date: 09/17/2003 at 11:01:40 From: Doctor Ian Subject: Re: prime and composite numbers Hi Hillary, Suppose I have 12 items, and I try to arrange them into a rectangle. I can do this in more than one way: . . . . . . . . . . . . 1 x 12 . . . . . . 2 x 6 . . . . . . . . . . 3 x 4 . . . . . . . . For some numbers, there is only one rectangle that I can make. For example, if I have 7 items, I can do this: . . . . . . . But if I try to make more rows, I always have something left over: . . . . . . . . . . . . . . . . . . . . . A number like 7 is called 'prime'. In contrast, a number like 12 is called 'composite'. One way to remember this is that something that is 'composed' is 'put together' from smaller pieces. (For example, we compose a poem from words, and compose a song from notes.) In the case of a number like 12, we can put it together in more than one way, using multiplication: 12 = 1 x 12 = 2 x 6 = 3 x 4 But 1 x 12 is hardly like putting something together, is it? So if we ignore ways that include a 1, we see that there are two ways to put together a 12, 12 = 2 x 6 = 3 x 4 and _no_ ways to 'put together' a 7. One tricky point is that the number 1 is considered to be neither prime nor composite. (Think about why this would be the case.) So while it's tempting to say things like A number is prime if it's not composite. or A number is composite if it's not prime. neither of these is quite true, because 1 isn't composite, but it's also not prime; and 1 isn't prime, but it's also not composite. Why do we care about any of this? That's discussed here: Why Study Prime and Composite Numbers? http://mathforum.org/library/drmath/view/57182.html Does this help? Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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