GCSE 1-3 Prime Factors and Trees Week 23

Identify Prime numbers, common factors,
common multiples
Use the concept of prime factorisation
Learning Objectives
Core Challenge Ultimate
Identify prime Explore Use appropriate
numbers mathematical methods to find
Identify common terminology used the highest
factors and in prime common factors
common multiples factorisation and lowest
Use the concept of common multiples
prime of two numbers
factorisation
2
Prime Numbers
Prime numbers have ONLY TWO FACTORS.
11 11  1, 11
2  1, 2 12  1, 2, 3, 4, 6, 12
3  1, 3 13  1, 13
4  1, 2, 4 14  1, 2, 7, 14
5  1, 5 15  1, 3, 5, 15
6  1, 2, 3, 6 16  1, 2, 4, 8, 16
7  1, 7 17  1, 17
8  1, 2, 4, 8 18  1, 2, 3, 6, 9, 18
9  1, 3, 9 19  1, 19
10  1, 2, 5, 10 20  1, 2, 4, 5, 10, 20
A prime number is a number where it’s only factors

are 1 and itself!
Prime Numbers
On the 1-100 grid, all the prime numbers are highlighted.
1 2 3 4 5 6 7 8 9 10
Anything in the 2
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
times table, 3 times
31 32 33 34 35 36 37 38 39 40
table, etc. has been
41 42 43 44 45 46 47 48 49 50 crossed off.
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 The numbers left are
71 72 73 74 75 76 77 78 79 80 prime!
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Can you remember the first 10 prime
numbers?
5
Common Factors
Factors are numbers that divide exactly
into another number.
Example: Find the common factors of 12 and 18
Factors of 12: Factors of 18:
1 2 3 4 6 12 1 2 3 6 9 18
Identify the common

factors
Common factors = 1,2,3 and 6

Common Multiples
Multiples are the numbers in the times
table.
Example: Find the first three common
multiples of 4 and 6
Multiples of 4 : 4,8,12,16,20,24,28,32,36,40…
Multiples of 6 : 6,12,18,24,30,36,42,48,54,60 …
Common multiples = 12,24 and 36 Identify the common

multiples
Worksheet 1
Factors, multiples and primes
10
Any number can be broken down into a string of prime
numbers all multiplied together – this is called
‘expressing it as a product of its prime

factors’,
Remember
or its PRODUCT means
multiplied
together!
‘prime factorisation’.
11
Factor Trees – Prime Factorisation
Express 50 as a product of its prime factors.
Step One Start with your number at
the top of the tree.
Step Two Branch out with factors.

10 5 Circle any
prime numbers.
5 2 Step Three Repeat this until finished.
Step Four All number circled will

12
x x = 50 = 52 x 2 multiple to make your
Factor Trees – Prime Factorisation
Express 18 as a product of it’s prime factors.
Step One Start with your number at
the top of the tree.
Step Two Branch out with factors.

9 2 Circle any
prime numbers.
3 3 Step Three Repeat this until finished.
Step Four All number circled will

13
x x = 18 = 32 x 2 multiple to make your
Your turn…..
54
27 2
9 3
As a product of its prime
numbers….
= 3x3x3x2
3 3
Or = 2 x
14
Worksheet 2
Factor Trees
15
When looking at Factors and Multiples we always look for the Highest
Common Factor (HCF) and the Lowest Common Multiple (LCM)
✘ HCF = The biggest number
that will divide into all the
✘ 36 and 54
numbers in the question
Method ✘ 36= 1, 2, 3, 4, 6, 9, 12,
1. List the factors of ALL the 18, 36
numbers
2. Find the biggest one that’s
in all the lists ✘ 54 = 1, 2, 3, 6, 9, 18, 27,
54
HCF =
16 12
When looking at Factors and Multiples we always look for the Highest
Common Factor (HCF) and the Lowest Common Multiple (LCM)
✘ LCM – the smallest

number that will divide
by all the numbers in 3 and 4
the question
Method 3, 6, 9, 12, 5, 18……
1. List the multiples of ALL
the numbers 4, 8, 12, 16……..
2. Find the smallest one
that’s in ALL the lists
LCM =
17
12
Finding the Highest Common Factor
42
Find the HCF of 56
and . Step One Find the prime factors
using prime factorisation.
7 6 7 8 Step Two Place numbers into a

Venn diagram.
3 2 4 2
2 2 Step Three Multiple all numbers in

the centre section. Duplicate
42 56 factors
combine in
the centre
Answer = 7 x 2 = 14 section.
HC
F
18
Finding the Lowest Common Multiple
42
Find the LCM of 56
and . Step One Find the prime factors
using prime factorisation.
7 6 7 8 Step Two Place numbers into a

Venn diagram.
3 2 4 2
2 2 Step Three Multiple all numbers in

the Venn diagram. Duplicate
42 56 factors
combine in
the centre
Answer = 3 x 7 x 2 x 2 x 2 = 168 section.
LC
19 M
Worksheet 3
HCF LCM
20

GCSE 1-3 Prime Factors and Trees Week 23

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Identify Prime numbers, common factors,

Prime numbers have ONLY TWO FACTORS.

A prime number is a number where it’s only factors

Factors of 12: Factors of 18:

Identify the common

Common factors = 1,2,3 and 6

Common multiples = 12,24 and 36 Identify the common

‘expressing it as a product of its prime

Step Two Branch out with factors.

5 2 Step Three Repeat this until finished.

Step Four All number circled will

Step Two Branch out with factors.

3 3 Step Three Repeat this until finished.

Step Four All number circled will

✘ LCM – the smallest

7 6 7 8 Step Two Place numbers into a

2 2 Step Three Multiple all numbers in

7 6 7 8 Step Two Place numbers into a

2 2 Step Three Multiple all numbers in

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