1. Targeting Grade C GCSE Mathematics Number
Unit 5 Prime Factors, HCF and LCM

2. Can you… If not you need Find prime factors
Write a number as a product of its prime factors
Try a test
Find the Highest Common Factor (HCF)
Find the Lowest Common Multiple (LCM)
TOP: Review prime numbers, factors, multiples
Practice 1: Finding prime factors
Practice 2: Expressing numbers as products of prime factors
TAIL 1
Practice 3: Finding HCF
Practice 4: Finding LCM
TAIL 2
If not you need

3. From the following list, write down all the prime numbers:
TOP:
From the following list, write down all the prime numbers:
5, 11, 4, 9, 17, 27, 31, 6, 37, 21
Write all the factors of 24.
Write the first five multiples of 6.
Write all the prime numbers between 40 and 50.
Write the common factors of 24 and 36.
Write the first three common multiples of 3 and 5.
Lesson

4. Practice 1: Find the prime factors of the following: (the first
one is done for you!)
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. 32 25 72 65 14
Lesson

5. Practice 2: Write the following as products of their prime factors (the
first one is done again!)
36 = 2  18
= 2  2  9
= 2  2  3  3
= 22  32 24 64 56
100
124
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.
Lesson

6. TAIL 1 1 2 3 4 5 6 7 8 9 10 Are you ready for the answers ?
Write one factor of 12
1, 2, 3, 4, 6, 12
2, 3
Write one prime factor of 12
Write the 2nd multiple of 8 16
Give two common multiples of 6 and 8
24, 48, 72, etc.
Write two factors of 16
1, 2, 4, 8, 16
Write the 4th and 9th multiple of 6
24, 72
Write 40 as a product of its prime factors
2  2  2  5
Write all the factors of 6
1, 2, 3, 6
Give all the common factors of 6 and 8
1, 2
Write 15 as a product of its prime factors
Lesson
3  5

7. Practice 3: Find the highest common factors of the following
pairs of numbers (check out the first one!)
12 and = 2  6 16 = 2  8
= 2  2  = 2  2  4
= 2  2  2  2
HCF = 2  2 = 4
8 and 12
32 and 40
21 and 33
72 and 84
120 and 136
The HCF is found by finding the product of prime factors then looking for the common factors and multiplying them!
Lesson

8. Practice 4: Find the lowest common multiple of the following pairs of
numbers (look at number 1 first!)
18 and = 2  9 24 = 2  12
= 2  3  = 2  2  6
= 2  2  2  3
LCM = 24  3 = 72
25 and 35
10 and 12
8 and 12
16 and 22
15 and 42
The LCM is found by finding the product of prime factors then looking at the common factors and multiplying the biggest number you started with by any additional factors in the smaller number!
Lesson

9. TAIL 2 Are you ready for the answers ? 12 Find the HCF of 24 and 36
Find the LCM of 24 and 32
Find the HCF and LCM of 72 and 120
Write 720 as a product of its prime factors.
Hence, or otherwise, find the HCF and LCM of 720 and 84.
Express 840 as a product of its prime factors and write the answer in index form.
(2) 96
HCF = 24,
LCM = 360
24  32  5
HCF = 12
LCM = 5040
(5) 23  3  5  7
Lesson