1. Types of numbers BTEOTSSBAT:
Recognise even, odd, prime, square and triangle numbers
Understand the terms factor and multiples
Be able to express numbers in terms of the product of primes
Use prime factorisation to find LCM and HCF

2. Key terms Even Odd Multiple Factor Prime number Prime factors
Highest common factor
Least common factor

3. Even numbers
2, 4, 6, 8, …..
Odd numbers
1, 3, 5, 7, ….
Simon says: If you add up two odd numbers together (Odd + Odd), you always get an even number.
Tasha says: If you add up two even numbers together, you will always get an odd number.
Are they right?

4. What do you get from the following?
(a) Odd + Even
(b) Even x Even
(c) Odd x Odd
(d) Even x Odd
(e) Even - Odd
(f) Odd - Odd

5. Factors and multiples 15 5 10, 15, 20 are all multiples of 5
They are in the 5s multiplication table
5 is a factor of 15
5 divides exactly into 15
Is a factor of 15 5
Is a multiple of

6. Write down the first four multiples of ….
2 :
4, 6, 8, 10, 12
24, 36, 48, 60
12 :
14, 21, 28, 35, 12
7 :

7. The complete list of factors of 12 is
All the factors of 12 are all the whole numbers that divide exactly into 12.
The complete list of factors of 12 is
{1, 2, 3, 4, 6, 12} .

8. Prime numbers A prime number only has two factors: 1 and itself.
Is 143 prime?
Is 103 prime?
2 doesn’t go into it.
2 doesn’t go into it.
3? No
3? No
5? No
5? No
7? No
7? No
11? Yes
11? No
So 143 = 11  13 and isn’t prime.
So 103 is prime.

9. State whether or not each of the following is a prime number – give a reason for your answer
(d)
(e) 119

10. Product of primes
Writing a number as a “product of its prime factors” involves writing the number as a series of prime numbers multiplied together.
e.g. 36 = 2  18
= 2  2  9
= 2  2  3  3
Therefore, as a product of its prime factors, 36 = 2  2  3  3

11. 36 36 First few prime numbers: 2, 3, 5, 7, 11, 13, …. 2 36 2 18 2 18 9
36 = 2 x 2 x 3 x 3
36 = 2 x 2 x 3 x 3

12. Express the following numbers as products of their prime factors.
b) c) 352