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MULTIPLES, FACTORS, PRIMES,
SQUARES AND CUBES
Factors
The whole numbers that divide exactly into 20 are called factors of 20.
So 4 is a factor of 20 because 20 ÷ 4 = 5.
Examples
1
34
5
6
7
8
9
10
11
12
From the set of numbers above write down the numbers that are
factors of 48.
The numbers that are factors of 48 are 3, 4, 6, 8 and 12.
List all the factors of 36.
List all the factor pairs.
36 = 1 × 36
36 = 2 × 18
36 = 3 × 12
36 = 4 × 9
36 = 6 × 6
Write the factors in order.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Find the highest common factor (HCF) of 27 and 90.
List all the factors of each number.
Factors of 27 =
1
3
9
27
Factors of 90 =
1
2
3
5
6
9
10 15 18 30 45 90
Select the common factors.
The highest common factor of 27 and 90 is 9.
Multiples
The multiples of 8 are 8, 16, 24, 32, 40, ...
The multiples of 13 are 13, 26, 39, 52, ...
Examples
1
24
7
10
15
20 29 34 44 52
74
From the set of numbers above write down the numbers that are
multiples of 4.
The numbers that are multiples of 4 are 4, 20, 44 and 52.
Find the lowest common multiple (LCM) of 6 and 15.
List the multiples of each number.
Multiples of 6 =
6
12 18 24 30 36 42 48 54 60 66 72…
Multiples of 15 = 15 30 45 60 75 90 105 120 135 150 165…
Select the common multiples.
The lowest common multiple of 6 and 15 is 30.
Primes
A prime number is a number that has exactly two factors.
7 is a prime number because it has exactly two factors (1 and 7).
Examples
1
20
21
22
23
24
25
26 27
28 29 30
From the set of numbers above write down the numbers that are
prime.
The numbers that are prime are 23 and 29.
List all the prime factors of 84.
List all the factors of 84.
Factors of 84 =
1
2
3
4
6
7
12 14 21 28 42 84
Select the factors that are prime.
The prime factors of 84 are 2, 3 and 7.
Write 42 as the product of its prime factors.
42
42 can be written as 6 × 7.
7
6
6 can be written as 2 × 3.
2
3
42 = 2 × 3 × 7
Write 120 as the product of its prime factors.
120
120 can be written as
10 × 12.
12
10
10 can be written as 2 × 5.
12 can be written as 3 × 4.
2
5
4
3
4 can be written as 2 × 2.
2
120 = 2 × 5 × 3 × 2× 2
2
= 23 × 3 × 5
Find the highest common factor (HCF) and lowest common
multiple (LCM) of 42 and 120.
From example 3:
42 = 2 × 3 × 7
From example 4:
120 = 2 × 2 × 2 × 3 × 5
Write the prime factors on the diagram.
7
Prime factors of 42
2
3
2
2
5
Prime factors of 120
The HCF is the product of the numbers in the intersection = 2 × 3 = 6.
The LCM is the product of all the numbers on the diagram
= 7 × 2 × 3 × 2 × 2 × 5 = 840.
Square numbers
1×1=1
2×2=4
3×3=9
4 × 4 = 16
The numbers 1, 4, 9, 16… are called square numbers.
4 × 4 can be written as 42.
Example
15
32
49 53
62 71
81
94 100
From the set of numbers above write down the numbers that are
square numbers.
The numbers that are square numbers are 49, 81 and 100.
Cube numbers
1×1×1=1 2×2×2=8
3 × 3 × 3 = 27
The numbers 1, 8, 27, 64… are called cube numbers.
4 × 4 × 4 can be written as 43.
Example
17
24
25
125
200
216
From the set of numbers above write down the numbers that are
cube numbers.
The numbers that are cube numbers are 1, 125 and 216.