Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
GCSE Maths Starter 9
1) Describe the Correlation in
the scatter graph below..
2. Expand 5(x – 3)
3. Simplify y⁵ x y³
4. What is 304 ÷ 8
5. What is 60⁰C converted
into ⁰F?
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
• To identify factors, multiples, squares and
prime numbers
• To find the prime factor decomposition of
• positive integers
• To find the Highest Common Factor (HCF) and
the Least Common Multiple (LCM) of two
numbers
EXTN: To solve real life problems involving HCF
and LCM.(Grade C)
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
What are the first five multiples of:
3, 6, 9, 12, 15
a) 3
4, 8, 12, 16, 20
b) 4
11, 22, 33, 44, 55
c) 11
21, 42, 63, 82, 105
d) 21
A multiple of a number is what you get
when you multiply that number by
some other whole number.
Multiples are
Usually
Larger
Than
Individual numbers,
Possibly
Larger never
Ever
Smaller
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
Identify the prime numbers in the grid below. There
are 7 to find.
7
X 45
X 22
X
39
23
63
17
9
57
81
X
X
X
X
77
11
27
X
X 19 99
X
X 37
X1 69
X 2 49
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
Lowest Common Multiple – the lowest number
in two or more numbers’ times tables.
Q. Find the LCM of 4 and 6.
1. Write out the first six numbers the 4 and 6
times tables
2. Look for the first number that appears in
both lists.
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
Example LCM
Q. Find the LCM of 4 and 6
4  4, 8, 12, 16, 20, 24,….
6  6, 12, 18, 24, 30, 36,…
We want the LOWEST common multiple, so
the LCM of 4 and 6 is… 12
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
Find the LCM of the following:
a) 2 and 5
10
b) 3 and 4
12
c) 4 and 8
8
d) 5 and 6
30
e) 3 and 8
24
f) 4 and 9
36
g) 8 and 10
40
h) 4, 5 and 12.
60
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
What are the factors of:
1, 2, 4, 8, 16
a) 16
1, 2, 5, 6, 15, 30
b) 30
1, 2, 4, 8
c) 8
1, 7
d) 7
A factor is a whole number which divides
exactly into a whole number, leaving no
remainder.
A prime number has exactly two factors:
1, and the number itself.
Factors
Are
Certainly
Tiny
Or
Really
Small
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
• Highest Common Factor (HCF) – the
number that goes into two or more numbers
exactly.
• Write out all the factors for each number….
• Example: Find the HCF of 32 and 56
32  1, 2, 4, 8, 16, 32
56  1, 2, 4, 7, 8, 14, 28, 56
HCF = 8
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
Find the HCF of the following numbers:
a) 8 and 12
4
b) 9 and 15
3
c) 10 and 30
10
d) 18 and 33
3
e) 32 and 80
16
f) 60 and 108
12
g) 36, 64, and 76
4
h) 48, 60 and 84
12
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
• We can use a ‘factor tree’ to enable us to
write a number as “a product of its prime
factors”
• Each time you reach a prime number, you stop
and circle that number.
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
• Example: Write 84 as a product of its prime factors
84
2
42
2
• 84 = 2 x 2 x 3 x 7
• 84 = 22 x 3 x 7
21
3
7
• Now your turn: Write 42 as a product of prime factors.
Your turn…
1. Find the HCF of the
following:
a)
b)
c)
d)
e)
f)
18 and 28
16 and 40
42 and 90
40 and 63
20, 64 and 108
54, 90 and 162
2
8
6
1
4
18
2. Find the LCM of the
following:
a)
b)
c)
d)
e)
f)
4 and 5
8 and 12
6 and 9
12 and 15
5, 8 and 10
4, 7 and 9
20
24
18
60
40
252
3. Write the following as products of their prime factors.
a) 18
32
x2
b) 135
33 x 5
c) 154
2 x 7 x 11
d) 2310
2 x 3 x 5 x 7 x 11
Lesson 9 Factors, Multiples,
Primes and Squares.
Mathswatch 44/95/96
• To identify factors, multiples, squares and
prime numbers
• To find the prime factor decomposition of
• positive integers
• To find the Highest Common Factor (HCF) and
the Least Common Multiple (LCM) of two
numbers
EXTN: To solve real life problems involving HCF
and LCM.(Grade C)