## Mrs. Flynn's, Mr. Olmsted's and Mr. Snyder's 2013-2014 Fifth Grade Class

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## Math - Factors

Vocabulary

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. Factors can also be called divisors. 4 is a divisor of 12.

Products are 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. The product of 12 x 3 is 36.

Some numbers have many factors, while other numbers have only a few.  Prime numbers cannot 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.

Some skills we are working with:

Decomposing numbers is taking them apart.

So 14 + 17 can be thought of as 10 + 10 + 7 + 3 + 1

Or  12 x 15 can be thought of as 6x2x15 or 6x30

Composing them is just putting them back together.

Decomposing numbers often makes use of “friendly numbers” that can be any number people have familiarity with. (25, 10, 12 etc.)

Compressibility describes the idea that while we learn complex things it takes up a large portion of our brain and attention, but when we get it down it takes up very little… like riding a bike. This is why we can keep learning new and interesting math concepts and our brains don’t fill up!

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.

For more math pages see Olmsted's Math Links

Related games from class