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.
List the first few prime numbers:
2, 3, 5, 7, 11, 13, 17, 19... 56
2 is a prime number and a factor of 56 so 2 is a prime factor of 56.
Is 28 a prime factor? 2 28
This is called a factor tree.
All the red digits are prime factors of 56. 2
No, so repeat the process for 28. 14 2 7
56 is an even number so can be written as 2  something...
A product is the result of multiplying.
56 = 2  2  2  7

4. Example 2 Write 90 as a product of its prime factors.
Draw a factor tree: 90
List the first few prime numbers:
Is 45 a prime factor? 2 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. 3
This is not the only possible factor tree, but any factor tree should give the same end result! 3
45 is in the 5 times table.
90 = 2  3  3  5

5. 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 21 3 7
420 = 2  2  5  3  7

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 75
648
108

7. Answers
1. 72 72 2 36 2 18 2
2, 3, 5, 7, 11, 13, 17, 19... 9 3 3
72 = 2  2  2  3  3

8. Answers
2. 80 80 2 40 2 20 2 10
2, 3, 5, 7, 11, 13, 17, 19... 2 5
80 = 2  2  2  2  5

9. Answers
3. 75 75 3 25 5 5
2, 3, 5, 7, 11, 13, 17, 19...
75 = 3  5  5

10. Answers
4. 648
648 2
324 2
126 2 81
2, 3, 5, 7, 11, 13, 17, 19... 9 9 3 3 3 3
648 = 2  2  2  3  3  3  3

11. Answers
5. 108
108 2 54 2 27 3 9
2, 3, 5, 7, 11, 13, 17, 19... 3 3
108 = 2  2  3  3  3

12. End