Prime Numbers Eratosthenes Sieve By Monica Yuskaitis Eratosthenes

Prime Numbers Eratosthenes’ Sieve 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. Copyright © 2000 by Monica Yuskaitis

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

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

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

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

Definition 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

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

Hundreds Chart 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

1 – Cross out 1; it is not prime. 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

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

2 – Leave 2; cross out multiples of 2 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

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. 267 Total of digits = 15 3 divides evenly into 15 267 is a multiple of 3 Copyright © 2000 by Monica Yuskaitis

3– Leave 3; cross out multiples of 3 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

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

4– Leave 5; cross out multiples of 5 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

5– Leave 7; cross out multiples of 7 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

6–Leave 11; cross out multiples of 11 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

All the numbers left are prime 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Copyright © 2000 by Monica Yuskaitis 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100

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

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