1. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96

2. Expand 5(x – 3) Simplify y⁵ x y³ What is 304 ÷ 8
GCSE Maths Starter 9
1) Describe the Correlation in the scatter graph below..
What is 60⁰C converted into ⁰F?
Expand 5(x – 3)
Simplify y⁵ x y³
What is 304 ÷ 8

3. 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)

4. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
What are the first five multiples of: 3 4 11 21
Multiples are
Usually
Larger
Than
Individual numbers,
Possibly
Larger never
Ever
Smaller
3, 6, 9, 12, 15
4, 8, 12, 16, 20
11, 22, 33, 44, 55
21, 42, 63, 82, 105
A multiple of a number is what you get when you multiply that number by some other whole number.

5. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Identify the prime numbers in the grid below. There are 7 to find. X X X 7 7 39 45 22 23 23 X X X X 63 17 17 9 57 81 X X X 11 11 77 27 19 19 99 X X X 69 2 2 49 37 37 1

6. 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.
Write out the first six numbers the 4 and 6 times tables
Look for the first number that appears in both lists.

7. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Example LCM
Find the LCM of 4 and 6
 4, 8, 12, 16, 20, 24,….
 6, 12, 18, 24, 30, 36,…
We want the LOWEST common multiple, so the LCM of 4 and 6 is… 12

8. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Find the LCM of the following:
2 and 5
3 and 4
4 and 8
5 and 6
3 and 8
4 and 9
8 and 10
4, 5 and 12. 10 24 12 36 40 8 30 60

9. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
What are the factors of: 16 30 8 7
1, 2, 4, 8, 16
1, 2, 5, 6, 15, 30
1, 2, 4, 8
1, 7
Factors
Are
Certainly
Tiny Or
Really
Small
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.

10. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Highest Common Factor (HCF) – the LARGEST 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

11. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Find the HCF of the following numbers:
8 and 12
9 and 15
10 and 30
18 and 33
32 and 80
60 and 108
36, 64, and 76
48, 60 and 84 4 16 3 12 10 4 3 12

12. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Prime Factors
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.

13. Lesson 9 Factors, Multiples, Primes and Squares. Mathswatch 44/95/96
Example: Write 84 as a product of its prime factors
84 = 2 x 2 x 3 x 7
84 = 22 x 3 x 7
Now your turn: Write 42 as a product of prime factors. 84 2 42 2 21 3 7

14. Your turn… Find the HCF of the following: 18 and 28 16 and 40
Find the LCM of the following:
4 and 5
8 and 12
6 and 9
12 and 15
5, 8 and 10
4, 7 and 9 2 20 8 24 6 18 1 60 4 40 18
252
Write the following as products of their prime factors.
a) 18 b) c) d) 2310
33 x 5
32 x 2
2 x 3 x 5 x 7 x 11
2 x 7 x 11

15. 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)