1. Factorgrams means divide by 3 means divide by 5.
I want to show you how our knowledge of factors can produce some interesting geometric patterns. For example the number 15 has two prime factors, 3 and 5. We can set out a 'picture' or factorgram as follows.
          means divide by 3
      means divide by 5.
The factorgram 'finishes' at 1.
It makes a box or rectangle shape.

2. Find 3 other different numbers that fit the above factorgram shape.
Challenge 1:
Find 3 other different numbers that fit the above factorgram shape.
( any number which has two prime factors that only divide into the numbers once each. )
10 (2x5), 35 (5x7), 39 (3x13), 34 (2x17), 187 (11x17).
Challenge 2:
Draw the factorgrams for these numbers. Prime factors are given in brackets.
12 (2,3)
100 (2,5)
63 (3,7)
Challenge 3:
Create a starting number using this factorgram shape with the prime factors 3 & 5. ( 15 doesn’t count)

3. All the numbers so far have two prime factors, the natural question for a mathematician to ask is: What if there are 3 prime factors, such as 2, 3 & 5?
For example, using 30 (2 x 3 x 5) as the starting number: ÷2 ÷3 ÷5

4. The factorgram 'finishes' at 1.
The side wall and base of the 'cube' show the 2D factorgrams for 15, 6 and 10.
The last line reads 5, 3, 2 which are our prime factors (in reverse order).
The number of different 'pathways' from 30 to 1 is 6 which corresponds to all the different combinations (or orders) of the divisions

5. Challenge 4:
Draw the factorgrams for these numbers.
Prime factors are given in brackets.
42 (2,3,7)
70 (2,5,7)
165 (3,5,11)