Prime Factorisation
Factor Trees
What’s It All About?
You are going to learn:
How to write a number as the product of its prime
factors.
What skills should you have already?
You need to know what it means for a number to be
a prime number or a factor.
You need sound multiplication skills.
Example 1
Write 56 as a product of its prime factors.
List the first few prime
numbers:
2, 3, 5, 7, 11, 13, 17, 19...
56
2
This is called a factor tree.
All the red digits are prime
factors of 56.
2 is a prime number
and a factor of 56 so 2
is a prime factor of 56.
Is 28 a prime factor?
28
2
14
2
A product is the result
of multiplying.
56 = 2  2  2  7
No, so repeat the
process for 28.
7
56 is an even number
so can be written as 2
 something...
Example 2
Write 90 as a product of its prime factors.
Draw a factor tree:
90
List the first few prime
numbers:
2
Is 45 a prime factor?
45
No, so repeat the
process for 45.
2, 3, 5, 7, 11, 13, 17, 19...
5
9
90 is an even number.
45 is not an even
number.
45 is in the 5 times
table.
3
90 = 2  3  3  5
3
This is not the only
possible factor tree,
but any factor tree
should give the
same end result!
Example 3
Write 420 as a product of its prime factors.
Draw a factor tree:
420
2, 3, 5, 7, 11, 13, 17, 19...
2
210
2
105
5
420 = 2  2  5  3  7
21
3
7
Your Turn
Draw a factor tree and use it to write each of
the following as the product of its prime
factors.
1.
2.
3.
4.
5.
72
80
75
648
108
Answers
1. 72
72
2
36
2
2, 3, 5, 7, 11, 13, 17, 19...
18
2
9
3
72 = 2  2  2  3  3
3
Answers
2. 80
80
2
40
2
2, 3, 5, 7, 11, 13, 17, 19...
20
2
10
2
80 = 2  2  2  2  5
5
Answers
3. 75
75
3
25
5
2, 3, 5, 7, 11, 13, 17, 19...
75 = 3  5  5
5
Answers
648
4. 648
2
324
2
2, 3, 5, 7, 11, 13, 17, 19...
126
2
81
9
3
648 = 2  2  2  3  3  3  3
9
3 3
3
Answers
5. 108
108
2
54
2
2, 3, 5, 7, 11, 13, 17, 19...
27
3
9
3
108 = 2  2  3  3  3
3
End