Factorgrams

1. Factorgrams • 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. 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)