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

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

2, 4, 6, 8, ….. 1, 3, 5, 7, …. Even numbers Odd numbers 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?

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

Factors and multiples 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 Is a factor of Is a multiple of

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

Factors 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}.

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

State whether or not each of the following is a prime number – give a reason for your answer (a)113 (b)124 (c)257 (d) (e)119

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

First few prime numbers: 2, 3, 5, 7, 11, 13, … = 2 x 2 x 3 x = 2 x 2 x 3 x 3

Express the following numbers as products of their prime factors. a) 72 b) 108 c) 352