1. Prime Factorisation Factor Trees

2. 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.

3. Example 1 Write 56 as a product of its prime factors.
56 is an even number so can be written as 2  something...
List the first few prime numbers:
2, 3, 5, 7, 11, 13, 17, 19... 56 28
28 is not a prime number, so repeat the process 2
This is called a factor tree.
All the red digits are prime factors of 56. 2 14
14 is not a prime number, so repeat the process 2 7
A product is the result of multiplying.
7 is a prime number, so stop the process
56 = 2  2  2  7

4. Example 2 Write 81 as a product of its prime factors.
81 is an odd number and is divisible by prime number 3
List the first few prime numbers:
2, 3, 5, 7, 11, 13, 17, 19... 81 27
27 is not a prime number, so repeat the process 3
This is called a factor tree.
All the red digits are prime factors of 81. 3 9
9 is not a prime number, so repeat the process 3 3
A product is the result of multiplying.
3 is a prime number, so stop the process
81 = 3  3  3  3
This is not the only possible factor tree, but any factor tree should give the same end result!

5. Example 3
Write 420 as a product of its prime factors.
420 is an even number so can be written as 2  something...
420
List the first few prime numbers:
2, 3, 5, 7, 11, 13, 17, 19...
210 is not a prime number, so repeat the process
210 2
105 is not a prime number, so repeat the process
This is called a factor tree.
All the red digits are prime factors of 420. 2
105
35 is not a prime number, so repeat the process 3 35
7 is a prime number, so stop the process 5 7
A product is the result of multiplying.
420 = 2  2  3  5 x 7
This is not the only possible factor tree, but any factor tree should give the same end result!

6. Your Turn
Draw a factor tree and use it to write each of the following as the product of its prime factors. 72 80
108