#### Mathematics 1 ESO – Unit 3 FACTORS AND MULTIPLES page 30 activity 11

__The “Sieve of Eratosthenes”__

We put all the numbers below 40 (except number 1) on a table:

2 | 3 | 4 | 5 | 6 | 7 | 8 | |

9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |

33 | 34 | 35 | 36 | 37 | 38 | 39 |

__ __

__1 ^{st}__: we

**number 2 and we delete all the multiples of 2.**

*take*2 |
3 | 5 | 7 | ||||

9 | 11 | 13 | 15 | ||||

17 | 19 | 21 | 23 | ||||

25 | 27 | 29 | 31 | ||||

33 | 35 | 37 | 39 |

__ __

__2 ^{nd}__: we

**the next number not deleted, number 3 and we delete all the multiples of 3.**

*take*2 |
3 |
5 | 7 | ||||

11 | 13 | ||||||

17 | 19 | 23 | |||||

25 | 29 | 31 | |||||

35 | 37 |

__ __

__3 ^{rd}__: we

**the next number not deleted, number 5 and we delete all the multiples of 5.**

*take*2 |
3 |
5 |
7 | ||||

11 | 13 | ||||||

17 | 19 | 23 | |||||

29 | 31 | ||||||

37 |

We continue until all the numbers in the table are **taken** or deleted The

**numbers are the**

*taken***.**

*prime numbers*__Activity 11__

Do the Sieve of Eratosthenes for all the prime numbers below 100