GCSE
Mathematics
Targeting Grade C
Number
Unit 5 Prime Factors,
HCF and LCM
Can you…
If not you need
TOP: Review prime numbers,
factors, multiples
•Find prime factors
Practice 1: Finding prime factors
•Write a number as a product of its prime
factors
Practice 2: Expressing numbers as
products of prime factors
Try a test
TAIL 1
•Find the Highest Common Factor (HCF)
Practice 3: Finding HCF
•Find the Lowest Common Multiple (LCM)
Practice 4: Finding LCM
Try a test
TAIL 2
TOP:
(1)
From the following list, write down all the prime numbers:
5, 11, 4, 9, 17, 27, 31, 6, 37, 21
(2)
Write all the factors of 24.
(3)
Write the first five multiples of 6.
(4)
Write all the prime numbers between 40 and 50.
(5)
Write the common factors of 24 and 36.
(6)
Write the first three common multiples of 3 and 5.
Lesson
Practice 1:
Find the prime factors of the following: (the first
one is done for you!)
(1) 18
The factors are 1, 2, 3, 6, 9 and 18 and the prime
numbers of this group are 2 and 3, so the prime
factors of 18 are 2 and 3.
(2) 32
(3)
25
(4)
72
(5)
65
(6)
14
Lesson
Practice 2:
Write the following as products of their prime factors (the
first one is done again!)
(1) 36 = 2  18
=229
=2233
= 22  32
(2)
24
(3)
64
(4)
56
(5)
100
(6)
124
Lesson
See how the black number is split into
a prime factor and other number at
each stage, while the prime factors
already found are carried down.
TAIL 1
Lesson
Are you ready for
the answers ?
1
2
3
4
5
6
7
8
9
10
Write one factor of 12
1, 2, 3, 4, 6, 12
Write one prime factor of 12
2, 3
Write the 2nd multiple of 8
16
Give two common multiples of 6 and
8
Write two factors of 16
24, 48, 72, etc.
Write the 4th and 9th multiple of 6
24, 72
Write 40 as a product of its prime
factors
Write all the factors of 6
Give all the common factors of 6 and
8
Write 15 as a product of its prime
factors
1, 2, 4, 8, 16
2225
1, 2, 3, 6
1, 2
35
Practice 3:
Find the highest common factors of the following
pairs of numbers (check out the first one!)
(1) 12 and 16
12 = 2  6
=223
HCF = 2  2 = 4
(2)
8 and 12
(3)
32 and 40
(4)
21 and 33
(5)
72 and 84
(6)
120 and 136
Lesson
16 = 2  8
=224
=2222
The HCF is found by finding the product of
prime factors then looking for the common
factors and multiplying them!
Practice 4:
Find the lowest common multiple of the following pairs of
numbers (look at number 1 first!)
(1)
18 and 24
18 = 2  9
24 = 2  12
=233
=226
=2223
LCM = 24  3 = 72
The LCM is found by finding the product of prime
(2)
25 and 35
(3)
10 and 12
(4)
8 and 12
(5)
16 and 22
(6)
15 and 42
Lesson
factors then looking at the common factors and
multiplying the biggest number you started with by
any additional factors in the smaller number!
TAIL 2
Are you ready for
the answers ?
(1)
Find the HCF of 24 and 36
(1) 12
(2)
Find the LCM of 24 and 32
(2) 96
(3)
Find the HCF and LCM of 72 and 120
(3) HCF = 24,
LCM = 360
(4)
Write 720 as a product of its prime factors.
Hence, or otherwise, find the HCF and LCM
of 720 and 84.
(4) 24  32  5
HCF = 12
LCM = 5040
(5)
Express 840 as a product of its prime factors
and write the answer in index form.
Lesson
(5) 23  3  5  7