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**Prime Numbers Eratosthenes’ Sieve**

By Monica Yuskaitis

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**Eratosthenes (ehr-uh-TAHS-thuh-neez)**

Eratosthenes was the librarian at Alexandria, Egypt in 200 B.C. Note every book was a scroll. Copyright © 2000 by Monica Yuskaitis

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**Eratosthenes (ehr-uh-TAHS-thuh-neez)**

Eratosthenes was a Greek mathematician, astronomer, and geographer. He invented a method for finding prime numbers that is still used today. This method is called Eratosthenes’ Sieve. Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Eratosthenes’ Sieve A sieve has holes in it and is used to filter out the juice. Eratosthenes’s sieve filters out numbers to find the prime numbers. Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor Copyright © 2000 by Monica Yuskaitis

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**7 Definition 7 is prime because the only numbers**

Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7. Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Hundreds Chart On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row. Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

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 Copyright © 2000 by Monica Yuskaitis

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**1 – Cross out 1; it is not prime.**

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 Copyright © 2000 by Monica Yuskaitis

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**Remember all numbers divisible by 2 are even numbers.**

Hint For Next Step Remember all numbers divisible by 2 are even numbers. Copyright © 2000 by Monica Yuskaitis

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**2 – Leave 2; cross out multiples of 2**

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 Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Hint For Next Step To find multiples of 3, add the digits of a number; see if you can divide this number evenly by 3; then the number is a multiple of 3. 2 6 7 Total of digits = 15 3 divides evenly into 15 267 is a multiple of 3 Copyright © 2000 by Monica Yuskaitis

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**3– Leave 3; cross out multiples 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 Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Hint For the Next Step To find the multiples of 5 look for numbers that end with the digit 0 and 5. 385 is a multiple of 5 & 890 is a multiple of 5 because the last digit ends with 0 or 5. Copyright © 2000 by Monica Yuskaitis

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**4– Leave 5; cross out multiples of 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 Copyright © 2000 by Monica Yuskaitis

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**5– Leave 7; cross out multiples of 7**

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 Copyright © 2000 by Monica Yuskaitis

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**6–Leave 11; cross out multiples of 11**

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 Copyright © 2000 by Monica Yuskaitis

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**All the numbers left are prime**

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 Copyright © 2000 by Monica Yuskaitis

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**The Prime Numbers from 1 to 100 are as follows:**

2,3,5,7,11,13,17,19, 23,31,37,41,43,47, 53,59,61,67,71,73, 79,83,89,97 Copyright © 2000 by Monica Yuskaitis

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**Copyright © 2000 by Monica Yuskaitis**

Credits Clipart from “Microsoft Clip Gallery” located on the Internet at clipgallerylive/default.asp Copyright © 2000 by Monica Yuskaitis

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