# How do factor pairs relate to the dimensions of a rectangle?

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How do factor pairs relate to the dimensions of a rectangle?
What are square numbers?

What are factor pairs? A factor pair consists of two whole numbers that are multiplied to get a product. Ex: All of the factor pairs of 18 are: 1, 18 2, 9 3, 6

Factor Pairs and Rectangles
Factor pairs of a number can be used to make rectangles with a given area. For example, if you have 18 tiles that you want to arrange into a rectangle, you can use the factor pairs listed on the previous slide to determine the rectangles’ dimensions (the side lengths).

Factor Pairs and Rectangles (cont.)
It is possible to make 3 different rectangles with 18 tiles. 1 by 18 2 by 9 3 by 6 Can you make a square with 18 tiles? Explain.

Square Numbers A square number is a number that is a result of the product of a number multiplied by itself. A square number will have an odd number of factors. Ex: 9 is a square number because 3 ● 3 = 9. Since 9 is a square number, you can make a 3 by 3 square using 9 tiles. What other square numbers can you think of?

Square Numbers (cont.) The number that is multiplied by itself to produce a square number is called the square root of that number. The square root of 9 is 3 because 3 ● 3 = 9. The square root symbol is √. “The square root of 9” looks like √9.

Square Numbers (cont.) A shortcut for writing 3 ● 3 is to use an exponent. 3² or “three squared” may also be read as “3 to the power of 2” or “3 to the 2nd power”.

The First 15 Square Numbers
Perfect Square Factors 1 1 * 1 or * 2 or * 3 or * 4 or * 5 or * 6 or * 7 or * 8 or * 9 or * 10 or * 11 or * 12 or * 13 or * 14 or * 15 or 152

Square Numbers (cont.) Notice that square numbers run diagonally through the middle of a multiplication chart!

More Square Numbers Here is a list of more square numbers:

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