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What is a prime number? How to find prime numbers • A prime number can be divided only by itself and 1 with nothing left over. • It has exactly two factors. A factor is a whole number b which hi h di divides id iinto a target number b with ih no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, 12 because I can divide 12 by all of them with no remainder. Using the sieve of Eratosthenes. (Invented in Greece 2300 years ago but still works today!) • This means that 1 is not a prime number. © www.teachitprimary.co.uk 2012 15012 1 © www.teachitprimary.co.uk 2012 15012 2 How to use The Sieve of Eratosthenes. How to use The Sieve of Eratosthenes. 1 2 5 6 9 10 13 14 1 2 5 6 9 10 13 14 3 7 11 15 © www.teachitprimary.co.uk 2012 4 8 12 16 Begin with a number grid. It can contain as many numbers as you like. LLet’s start withh a small one. 15012 3 3 7 11 15 © www.teachitprimary.co.uk 2012 4 8 12 16 We are going to cross off all of the numbers that are NOT prime numbers. L Let’s start ffrom the h smallest number. Remember, 1 isn’t a prime number. 15012 4 How to use The Sieve of Eratosthenes. How to use The Sieve of Eratosthenes. 1 2 5 6 9 10 13 14 1 2 5 6 9 10 13 14 © www.teachitprimary.co.uk 2012 3 7 11 15 4 8 12 16 15012 Now we’ll look at the next smallest number which is 2. We need to circle it as it is a prime number. Next we blot out all of the numbers which are multiples of 2. 5 © www.teachitprimary.co.uk 2012 3 7 11 15 4 8 12 16 15012 Ok, 3 is the next smallest number now. We need to circle it. Now we blot out all the h multiples l l off 3 3. 6 1 How to use The Sieve of Eratosthenes. 1 2 5 6 9 10 13 14 © www.teachitprimary.co.uk 2012 3 7 11 15 4 8 12 16 15012 The sieve of Eratosthenes is simple, yet very clever. It can be used to work out any prime numbers, as long l as you hhave patience. Try to explain how we can be sure that it works – what is going on? 7 2