Activity 4.1: Factors & Rectangles

Factors and Rectangles

Purpose: Explore the ideas of factor, prime, and composite.

Materials: Small squares or Color Tiles App Links to an external site.

1. Get 4 squares and make as many different rectangles as you can using all 4 squares. Record the dimensions of each rectangle as Width x Height, and write each down in order by the width.
   For example, with 4 squares:
   
   So, 4 squares can make the following rectangles:  1x4, 2x2, 4x1.
   
   
2. Repeat this for each of the following numbers, completing the table below.
   

   Number	Rectangle list (WxH)	Number of Rectangles
   1
   2
   3
   4	1x4, 2x2, 4x1	3
   5
   6
   7
   8
   9
   10
   11
   12

   
   
   
3. List the numbers that made only 1 rectangle.
   
   
   
4. List the numbers that made only 2 rectangles.
   
   
   
5. List the numbers that made more than 2 rectangles.
   
   
   
6. List the numbers that made an odd number of rectangles.
   
   
   
7. Complete the following table:
   

   Number	List of Factors	Number of Factors
   1
   2
   3
   4
   5
   6
   7
   8
   9
   10
   11
   12

   
   
   
8. Factor 24:
   1. List all of the factors of 24.
      
      
   2. State a factorization of 24.
      
      
   3. State the prime factorization of 24.
      
      
      
9. Factor 51:
   1. List all of the factors of 51.
      
      
   2. State a factorization of 51.
      
      
   3. State the prime factorization of 51.
      
      
      
10. Factor 53:
    1. List all of the factors of 53.
       
       
    2. State a factorization of 53.
       
       
    3. State the prime factorization of 53.
       
       
       
11. What type of numbers have exactly 2 factors?
    
    
    
12. What type of numbers have more than 2 factors?
    
    
    
13. What type of numbers have an odd number of factors?