m6 3 prime numbers eratosthenes sieve

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Prime NumbersEratosthenes’ Sieve

By Monica Yuskaitis



Copyright © 2000 by Monica Yuskaitis

Eratosthenes

(ehr-uh-TAHS-thuh-neez)

Eratosthenes was the librarian at

Alexandria, Egypt in 200 B.C.

Note every book was a scroll.




Eratosthenes

(ehr-uh-TAHS-thuh-neez)Eratosthenes was a Greekmathematician, astronomer, andgeographer.He invented a method for finding

prime numbers that is still used today.

This method is called Eratosthenes’Sieve.




Eratosthenes’ Sieve

A sieve has holes in it and is used tofilter out the juice.

Eratosthenes’s sieve filters out

numbers to find the prime numbers.




DefinitionFactor – a number that is

multiplied by another to give a product.

7 x 8 = 56Factors




DefinitionFactor – a number that

divides evenly into another.

56 ÷ 8 = 7

Factor


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DefinitionPrime Number – a number that

has only two factors, itself and 1.

7

7 is prime because the only numbersthat will divide into it evenly are 1 and 7.



Hundreds Chart

On graph paper, make a chart of

the numbers from 1 to 100, with 10numbers in each row.



1 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 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Hundreds Chart



1 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 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 – Cross out 1; it is not prime.



Hint For Next Step

Remember all numbers

divisible by 2 are even numbers.



1 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 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

2 – Leave 2; cross out multiples of 2




Hint For Next Step

To find multiples of 3, add thedigits of a number; see if you can

divide this number evenly by 3;then the number is a multiple of 3.

2 6 7Total of digits = 15

3 divides evenly into 15

267 is a multiple of 3




1 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 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100





To find the multiples of 5 look

for numbers that end with the

digit 0 and 5.

Hint For the Next Step

385 is a multiple of 5

& 890 is a multiple of 5 because the last digit

ends with 0 or 5.




1 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 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100





1 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 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

All the numbers left are prime




The Prime Numbers from 1 to

100 are as follows:

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,

53,59,61,67,71,73,79,83,89,97




CreditsClipart from “Microsoft Clip

Gallery” located on the Internetat http://cgl.microsoft.com/

clipgallerylive/default.asp

http://cgl.microsoft.com/

http://cgl.microsoft.com/

m6 3 prime numbers eratosthenes sieve

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