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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.
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.
77 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
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
Copyright © 2000 by Monica Yuskaitis
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.
Copyright © 2000 by Monica Yuskaitis
Hint For Next Step
Remember all numbers divisible by 2 are even numbers.
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
Hint For Next StepTo 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 7Total of digits = 15
3 divides evenly into 15267 is a multiple of 3
Copyright © 2000 by Monica Yuskaitis
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
3– Leave 3; cross out multiples of 3
Copyright © 2000 by Monica Yuskaitis
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 digitends with 0 or 5.
Copyright © 2000 by Monica Yuskaitis
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
4– Leave 5; cross out multiples of 5
Copyright © 2000 by Monica Yuskaitis
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
5– Leave 7; cross out multiples of 7
Copyright © 2000 by Monica Yuskaitis
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
6–Leave 11; cross out multiples of 11
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
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
