prime numbers

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 Greek mathematician, astronomer, and geographer.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 to filter out the juice.Eratosthenes’s sieve filters out numbers to find the prime numbers.


Definition

Factor – a number that is multiplied by another to give a product.

7 x 8 = 56

Factors


Definition

Factor – a number that divides evenly into another.

56 ÷ 8 = 7

Factor


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.


Hundreds Chart

On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.


1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

Hundreds Chart


1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 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 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

2 – Leave 2; cross out multiples of 2


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


1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

3– Leave 3; cross out multiples of 3


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.


1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100



1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

6–Leave 11; cross out multiples of 11


1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 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


Credits

Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/clipgallerylive/default.asp

http://cgl.microsoft.com/

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