Finding the Factors of a NumberDate: 09/24/2001 at 17:22:11 From: Kourtney Dubbs Subject: I need to know what factor is I need to know how to find the factor of a number. Date: 09/25/2001 at 16:49:05 From: Doctor Ian Subject: Re: I need to know what factor is Hi Kourtney, Every number greater than 1 has at least two factors: 1 and itself. For example, 2 = 1 * 2 3 = 1 * 3 4 = 1 * 4 and so on. That is, two numbers are 'factors' of another number if you can multiply them together to get that number. Note that 4 has some other factors besides 1 and 4: 4 = 1 * 4 4 = 2 * 2 But these are the only factors of 4. A number like 36, on the other hand, has _lots_ of factors: 36 = 1 * 36 = 2 * 18 = 3 * 12 = 4 * 9 = 6 * 6 Now, how can I _find_ those factors? Well, I start with the ones that _have_ to be there, 1 and 36: 36 = 1 * 36 Next, I try dividing by the next highest number after 1, which is 2. 2 goes into 36 18 times, so 2 and 18 are a pair of factors: 36 = 1 * 36 = 2 * 18 So then I just keep trying more numbers: 36 = 1 * 36 = 2 * 18 = 3 * 12 = 4 * 9 Now, note that 5 doesn't work, so I leave that out, and go on to 6: 36 = 1 * 36 = 2 * 18 = 3 * 12 = 4 * 9 = 6 * 6 Again, 7 doesn't work, and neither does 8. But 9 works: 36 = 1 * 36 = 2 * 18 = 3 * 12 = 4 * 9 = 6 * 6 = 9 * 4 but it would be silly to add that to my table, because it says the same thing as an earlier entry: 36 = 1 * 36 = 2 * 18 = 3 * 12 = 4 * 9 <--+ = 6 * 6 | the same factors = 9 * 4 <--+ So I know that I'm done. Any numbers larger than 6 will match up with something smaller than 6. So the factors of 36 are 1, 36, 2, 18, 3, 12, 4, 9, and 6. Note that if you don't like to think about division, you can find factors another way. Imagine that we have 36 cookies, and we'd like to arrange them into rectangles. How many different ways can we do that? @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ 36 by 1 @@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@ 18 by 2 @@@@@@@@@@@@ @@@@@@@@@@@@ @@@@@@@@@@@@ 12 by 3 @@@@@@@@@ @@@@@@@@@ @@@@@@@@@ @@@@@@@@@ 9 by 4 @@@@@@ @@@@@@ @@@@@@ @@@@@@ @@@@@@ @@@@@@ 6 by 6 Do you see why this is really the same thing we were doing before with division? For example, there is no way to arrange 8 rows of cookies to get a rectangle with 36 cookies; this is the same as saying that 36 isn't divisible by 8. Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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