Product Equal to 12Date: 04/09/2003 at 17:44:21 From: Jan W. Pollard Subject: How many different numbers have a product equal to 12? How many different numbers have a product equal to 12? I need an elementary example. What type of math is this called? Date: 04/10/2003 at 15:50:43 From: Doctor Ian Subject: Re: How many different numbers have a product equal to 12? Hi Jan, This is called 'factoring'. If the product of two numbers is another number, then the first two are factors of the third. For example, Product Factors ------- ------- 12 1, 12 because 1*12 = 12 12 2, 6 2*6 = 12 12 3, 4 3*4 = 12 So the factors of 12 are 1, 2, 3, 4, 6, 12 The simplest way to find the factors of any number is to start dividing it by every smaller number. If you get no remainder, it's a factor. For example, 12/1 = 12 (no remainder) So 1 is a factor 12/2 = 6 (no remainder) So 2 is a factor 12/3 = 4 (no remainder) So 3 is a factor 12/4 = 3 (no remainder) So 4 is a factor 12/5 = 2 (remainder 2) 12/6 = 2 (no remainder) So 6 is a factor 12/7 = 1 (remainder 5) 12/8 = 1 (remainder 4) 12/9 = 1 (remainder 3) 12/10 = 1 (remainder 2) 12/11 = 1 (remainder 1) 12/12 = 1 (no remainder) So 12 is a factor Now, if you do this for a few numbers, you should quickly see some patterns. For example, once you get up to half the product, you never find any more factors until you get to the product itself. Can you see why that has to be true? So you can stop dividing when you get halfway to the product. A second pattern is this: factors come in pairs. So in the example above, when I divided by 3 and got 4, with no remainder, that told me that I didn't really need to divide by 4. Why? Because I'd get 3 with no remainder. Similarly for 2 and 6. Of course, for a big number like 100, that's a lot of dividing. And as you might expect, mathematicians have figured out ways to eliminate most of the work, by using 'prime factors'. You can read about how to do that here: Finding All the Factors of 100 http://mathforum.org/library/drmath/view/58525.html and here: Why Study Prime and Composite Numbers? http://mathforum.org/library/drmath/view/57182.html and Prime Factoring http://mathforum.com/library/drmath/sets/shortcuts/ dm_prime_factors.html Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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