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Open: draw and colour-code factor
trees for three numbers between
150 and 200.
Show that you con grow 4 other
foctor trees for 60 in this way.
~
The tree in~ has 4 prime foctors.
Design a factor tree with at least 6 prime factors.
tree ~ a 2 x 2 x 5 x 5 = 1 00
tree ~ b 2 x 2 x 2 x 2 x 2 x 2 = 64
• Multiply two or more of these together
b Explain what is special about to try to make the products below. tree ~ c 2 x 2 x 3 x 2 x 5 = 1 20
the product each time. 18 28 35 42 52 63
84 85 99 175 380 490 tree ~ d 3 x 3 x 2 x 2 x 2 = 72
@] Drow factor trees for these numbers.
Use a colour key to show prime factors. • Use a calculator ii it helps. In the same way, check that the
Yes, 2 is the missing factor.
products of the prime factors equal
the root number for each tree in~.

In tree a, f = 5 e = 3 In tree b, p = 2 or 5 q = 5 or 2 r= 3
In tree c, w = 2 x = 2 Z= 2 y= 4 U= 2 V= 2
Possible combinations (the parantheses indicate that the number is not a
prime number, so it will have further branches coming off):

60 = 2 x (30) = 2 x 3 x ( 1 0) = 2 x 3 x 2 x 5 60 = (4) x (15) = 2 x 2 x 3 x 5
a tree 1 a tree 1 b tree 1 c
60 = 2 x (30) = 2 x 2 x ( 15) = 2 x 2 x 3 x 5 60 = 5 x (12) = 5 x 2 x (6) = 5 x 2 x 3 x 2
5 x 3 x 3 = 45 2 x 5 x 3 x 2 = 60 2 x 2 x 2 x 2 x 2 = 32
60 = 2 x (30) = 2 x (6) x 5 = 2 x 2 x 3 x 5 60 = 5 x (12) = 5 x 3 x (4) = 5 x 3 x 2 x 2
b The product of all the prime factors is the 'root' number. 60 = 3 x (20) = 3 x 2 x ( 1 0) = 3 x 2 x 2 x 5
60 = 3 x (20) = 3 x (4) x 5 = 3 x 2 x 2 x 5

Challenge
Possible solutions:
Open: design a possible products impossible products
factor tree 2x3x3= 18 52
with at least 2 x 2 x 7 = 28 85
six prime 5 x 7 = 35 qq
factors. 2 x 3 x 7 = 42 380
One possible 3 x 3 x 7 = 63
solution: 2 x 2 x 3 x 7 = 84
5 x 5 x 7 = 175
2 x 5 x 1 x 1 = 4qo