Rectangles and Factors

In class today we looked at the relationship between rectangles and factors.  If we look at the number 12 in terms of area of a rectangle, we know that area is equal to length times width, or a = l x w.  So for an area of 12 we can see that

 12x1  1x12  2x6  6x2  3x4  4x3

are possibilities that would give us an area of 12.  Two numbers multiplied together are called a factor pair.  This means each individual number in a factor pair is a factor.  In this case, the factors of 12 are:

1, 2, 3, 4, 6, and 12.

The dimensions of an rectangle are also the factors of the area of that rectangle.  This is important in helping us find both factors and area of numbers.

In describing factors, we use a few terms to determine what type of number we are dealing with which also allows use to make generalizations and "rules" so to speak.

Even-numbers that have 2 as a factor.
Prime-numbers that have only 2 factors, 1 and itself
Square-also called perfect squares because the have a factor pair that makes a square in terms of area; numbers who have an odd number of factors (ex: 4, 9, 16, 25.  factors of 25 are 1, 5, and 25)
Composite-numbers that have more than 2 factors (3 or more factors make a number composite.
Abundant-"more than enough"; numbers whose proper factors when added together are greater than the number itself (ex: 30, with the proper factors being 1, 2, 3, 5, 6, 10, and 15 adding up to 42)
Deficient-:"not enough"; numbers whose proper factors when added together are less than the number itself (ex: 15, with proper factors of 1, 3, and 5 adding up to 8)
Perfect-"exactly right"; numbers who proper factors when added together equal the number itself (ex: 28, with proper factors of 1, 2, 4, 7, and 14 adding up to 28)





Tomorrow in class we will have a quiz.  I went over what to expect on the quiz.  Each student should have written down a study guide like information sheet.  This picture goes with it.