Prime FactorisationFactor 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.

List the first few prime numbers:

2, 3, 5, 7, 11, 13, 17, 19...

List the first few prime numbers:

2, 3, 5, 7, 11, 13, 17, 19...

Write 56 as a product of its prime factors.

Example 1

56

2 28

2 14

2 7

56 = 2 2 2 756 is an even number so can be written as 2

something...

56 is an even number so can be written as 2

something...

A product is the result of multiplying.

A product is the result of multiplying.

2 is a prime number and a factor of 56 so 2 is a prime factor of 56.Is 28 a prime factor?

2 is a prime number and a factor of 56 so 2 is a prime factor of 56.Is 28 a prime factor?

No, so repeat the process for 28.

No, so repeat the process for 28.

This is called a factor tree.All the red digits are prime

factors of 56.

This is called a factor tree.All the red digits are prime

factors of 56.

List the first few prime numbers:

List the first few prime numbers:

Write 90 as a product of its prime factors.Draw a factor tree:

Example 2

90

2 45

5 9

3 3

90 = 2 3 3 5

90 is an even number.90 is an even number.

2, 3, 5, 7, 11, 13, 17, 19...

Is 45 a prime factor?Is 45 a prime factor?

No, so repeat the process for 45.

No, so repeat the process for 45.

45 is not an even number.

45 is not an even number.

45 is in the 5 times table.

45 is in the 5 times table.

This is not the only possible factor tree, but any factor tree

should give the same end result!

This is not the only possible factor tree, but any factor tree

should give the same end result!

Write 420 as a product of its prime factors.Draw a factor tree:

Example 3

420

2 210

2 105

5 21

420 = 2 2 5 3 7

2, 3, 5, 7, 11, 13, 17, 19...

3 7

Draw a factor tree and use it to write each of the following as the product of its prime factors.

1. 722. 80 3. 75 4. 6485. 108

Your Turn

1. 72

Answers72

2 36

2 18

2 9

3 3

72 = 2 2 2 3 3

2, 3, 5, 7, 11, 13, 17, 19...

2. 80

Answers

80 = 2 2 2 2 5

2, 3, 5, 7, 11, 13, 17, 19...

80

2 40

2 20

2 10

2 5

3. 75

Answers

75 = 3 5 5

2, 3, 5, 7, 11, 13, 17, 19...

75

3 25

5 5

4. 648

Answers

648 = 2 2 2 3 3 3 3

2, 3, 5, 7, 11, 13, 17, 19...

648

2 324

2 126

2 81

9 9

3 3 3 3

5. 108

Answers

108 = 2 2 3 3 3

2, 3, 5, 7, 11, 13, 17, 19...

108

2 54

2 27

3 9

3 3

End