Prime Factorisation Factor Trees

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Prime FactorisationFactor Trees
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Whats 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.
No, so repeat the process for 28.
2
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
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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.
This is not the only possible factor tree, but
any factor tree should give the same end result!
3
3
45 is in the 5 times table.
90 2 ? 3 ? 3 ? 5
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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
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Your Turn
Draw a factor tree and use it to write each of
the following as the product of its prime factors.

1. 72
2. 80
3. 75
4. 648
5. 108

7
Answers
1. 72
72
2
36
2
18
2
9
2, 3, 5, 7, 11, 13, 17, 19...
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
648
4. 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
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End