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Mrs. Flynn's, Mr. Olmsted's and Mr. Snyder's 2012-2013 Fifth Grade Class |
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Math - FactorsUnderstanding Factors
Factors are numbers that can divide evenly into another number. 4 is a factor of 12. In the multiplication problem 4x3=12, 4 and 3 are called factors and 12 is called a product. Products can thus be defined as the answer to a multiplication problem. Products are also considered multiples of each factor. For instance, 12 is a multiple of 4. 12 is also a multiple of 3. Some numbers have many factors, while other numbers have only a few. Prime numbers can not be divided evenly by any numbers except for 1 and the number itself. Prime numbers include 2,3,5,7,11,13,17,19 and so on. Composite numbers on the other hand have more than 2 factors. 6 can be divided by 1,2,3, and 6. This is what makes 6 a composite number. Examine Mr. Olmsted's Factor Pair Mountain The following diagram illustrates the concept of the Factor Pair Mountain for the number 110. Each pair of factors multiply together to get 110. You can make similar mountains for any number you choose.
 Every factor has a factor pair.
These two numbers multiply together to make the product, which in this
case is 110. When searching for factors, you can use this knowledge to
ensure that you have found all of the factors for a number.
To find factors, you need to use a system! Start with ONE and work your way to Factor Pair Mountain Summit. You will know you've reached the summit when two consecutive factors form number you are looking for. 10 times 11 is 110, so this is the mid-point, or summit. Now just find the factor pair for each number you found on the way up. Important: Notice that all of the high factors of 110 (22 and 55) are paired with low factors. This is intuitive, but also instructive. In fact, all factors fall evenly on both sides of the square root of the number you are factoring. This means that if you enter the number into a calculator and press the square root button, all of the factors you need to check are below that number. When you find one factor, you should then have its pair. (Divide one factor into your number to get the pair.) All factors are whole numbers, which have no fractional (decimal) component. |
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