# Factor Trees

*Keywords:*

AO elaboration and other teaching resources

Solve problems by finding the prime factors of numbers.

Number Framework Stage 8

#### Using Number Properties

Problem: “Barry wants to factorise 36. He notes the following:

36 = 2 x 18, 36 = 4 x 9, 36 = 6 x 6. He draws a complete factor tree for 36 = 2 x 18 as shown.

Draw factor trees that start at 36= 4 x 9, then 36 = 6 x 6.”

Discuss why the ends of the trees *all *show 36 = 2 x 3 x 3 x 2.

Examples: Noting 24 = 2 x 12, 24 = 8 x 3, 24 = 6 x 4, draw factor trees that *all *show 24 = 2 x 2 x 2 x 3 at the end.

Noting 30 = 3 x 10, 30 = 6 x 5, 30 = 2 x 15, draw factor trees that *all *show 30 = 2 x 3 x 5 at the end.

Problem: “Julia wants to factorise 144. She decides to use divisibility rules. 2 is a factor of 144, so 144 = 2 x 72. 2 is a factor of 72, so 72 = 2 x 36. Julia continues testing divisibility by 2 until she arrives at 18 = 2 x 9. She notes 9 = 3 x 3, and so she stops. Follow Julia’s steps, which show 144 = 32 x 24. Use a factor tree if this helps.”

Examples: Reduce these numbers to their prime factors. Use the power notation for the answers: 180, 120, 1 000

#### Understanding Number Properties:

Make up a number of your own over 150 and reduce it to its prime factors.