3. Be able to express numbers in terms of the product of primes
4.
5. 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?
6. 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
7. 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 15 Is a factor of 15 5 Is a multiple of
8. Write down the first four multiples of …. 2 : 4, 6, 8, 10, 12 24, 36, 48, 60 12 : 14, 21, 28, 35, 12 7 :
9. 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} .
10. 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.
11. 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) 134783 (e) 119
12. 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
13. First few prime numbers: 2, 3, 5, 7, 11, 13, …. 36 36 36 2 18 2 2 18 9 2 3 9 3 3 3 3 1 36 = 2 x 2 x 3 x 3 36 = 2 x 2 x 3 x 3