This lesson will help students who are starting to learn about factors. A factor is a number you use to multiply. In the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since they can be used in a multiplication equation to make 56. (56, the answer, is called the product.)

A factor is a number you use to multiply.
In the math equation:

8 x 7 = 56,

the 8 and the 7 are both factors of 56,
since they can be used in a multiplication equation to make 56.
(56, the answer, is called the product.)

In this lesson we will use square tiles to help figure out the factors of a whole number. In the example below we will use 18 to help us figure out the factors of 18.

We will arrange the square tiles into sets with rows and columns. These sets are called arrays.

Find as many different arrays as you can, but follow one important rule: all the rows MUST have the same number of tiles in every row. | |||

I can make one row of 18, so 1 and 18 are both factors of 18. |
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I can make two rows of nine, so 2 and 9 are both factors of 18. |
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I can make three rows of six, so 3 and 6 are both factors of 18. |
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I can make four rows, but they don't come out evenly with the same number in each row, so 4 is NOT a factor of 18. |
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I can make five rows, but they don't come out evenly, so 5 is NOT a factor of 18. |
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I can make six rows of three. I already have 6 and 3 on my list of factors. |
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As soon as you get factors that are already on your list, you can stop. All the factors you find will now be repeats of factors you already have. However, you might want to prove to yourself that there are no more factors by arranging the tiles in the remaining arrays. | |||

7 rows |
8 rows |
(9 & 2 already on the list) 9 rows |
10 rows |

11 rows |
12 rows |
13 rows |
14 rows |

15 rows |
16 rows |
17 rows |
(18 & 1 already on the list) 18 rows |

So, I have used my 18 square tiles to find the factors of 18. The arrays that worked were: - 1 x18 (repeated as 18 x 1)
- 2 x 9 (repeated as 9 x 2)
- 3 x 6 (repeated as 6 x 3)
I write the factors in order from smallest to greatest, so the factors of 18 are: 1, 2, 3, 6, 9, and 18. |

When you finish making your list of the arrays that work, (or the multiplication equations if you use your knowledge of facts rather than using tiles), draw a smile because you're done!

Now follow the smile around from left to right to write down all the factors. They will already be in order from least to greatest!

1 , 2 , 3 , 6 , 9 , 18

18 is a composite number. It smiles! Numbers that have at least four factors (two multiplication equations that work) form a smile. These numbers are called “Composite Numbers”. | |

Numbers that have only one and themselves as factors (one multiplication equation that works) form a straight line. These numbers don't form a smile. These numbers are called "Prime Numbers". |

- Factors (3-page worksheet with Guided Practice)
- Factors (Prime and Composite Numbers) (3-page worksheet with Guided Practice)