Factor tiles (Investigation)

Objectives

• To visualise the prime factorisation of numbers.
• To discover the highest common factor and least common multiple of numbers.
• To practise making factor trees.

Materials

• 3 copies of the factor tiles (below)
• Crayons & other drawing tools
• Scratch Paper 
• Construction paper (2 pieces)

Procedure

Work in small groups or on your own.

1. Print and cut out all of the prime factor tiles.
2. Use the blocks to model factors of a number. If multiple smaller blocks line up with a larger one, then the smaller number is a factor of the larger.  For example, 5 is a factor of 10 because two 5 blocks line up with one 10 block.  Note: If you have to use more than one different type of block for them to line up, then the smaller numbers are not factors.  
3. See how many ways you can use the smaller blocks to create the number 20. When you do this line up the blocks side by side so you can clearly see they are equal.
4. Use the factor blocks to find the prime factors of each of the following numbers: 
   • 80
   • 40
   • 25
   • 50
   • 30 
5. Write down all of the factors for each. 
6. Using what you found from the factor blocks create a factor tree on your construction paper for two of the numbers above. You can be creative with how you represent your factor tree and choose to use flowers or vines as long as it is in the correct format.

Follow-Up Questions:

1. What was the highest common factor of your two numbers? How could you use the factor tiles to help you find this number?

2. What was the least common multiple of your two numbers? How could you use the factor tiles to help you find this number?