http:// sieve of eratosthenes

http://www.mathslideshows.com

Sieve of Eratosthenes


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 the Sieve ofEratosthenes.

Eratosthenes(ehr-uh-tahs-thuh-neez)


Sieve of Eratosthenes

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.


FACTORA Factor is a number that ismultiplied by another number togive the product.

7 x 8 = 56

Factors


FACTORA Factor is the number thatdivides evenly into another.

56 ÷ 8 = 7

Factor


PRIME NUMBERA Prime Number is a number thathas only two factors, itself and 1.

77 is prime because the only

numbersthat will divide into it evenly are

1 and 7.


Hundreds ChartI am going to give you a

hundredschart with the numbers from 1 to100, with 10 numbers in each row.You are going to use the Sieve of Eratosthenes to discover the prime numbers between 1 and 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

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 numbersdivisible by 2 are evennumbers. Remember theyend in 0, 2, 4, 6, 8…


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 StepTo find multiples of 3, add the digits ofa number. If the sum divides evenly by3 then the number is a multiple of 3.

2 6 7Add the digits: 2 + 6 + 7 = 15 15 is divisible by 3 so

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



Hint For the Next StepRemember the number 4 is amultiple of 2 and an even number. You don’t have to domultiples of 4 since you alreadycrossed off multiples of 2.


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 5and 890 is a multiple

of 5because 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



Hint For the Next StepRemember a number isdivisible by 6 if it is divisibleby 2 and 3. Since you have already crossed out multiples of 2 and 3 then you have already done multiples of 6.


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



Hint For the Next StepRemember the number 8 is a multiple of 2 , the number 9 is a multiple of 3, and the number 10 is a multiple of 2. What number do you think is next?


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

The leftover numbers are prime 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

Circle the rest of the primes on your chart.


The Prime Numbers from 1 to 100 are as follows: Write these down on the bottom of your paper:

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

A prime number is a number that has no factors other than 1 and itself.

There are 25 prime numbers from 0 to 100.Check your list to make sure you have them all!


Composite numbers have more than 2 factors.PRIME FACTORIZATION is the unique set of prime numbers whose product equals a given number.

Write the prime factorization for the following.

24 24FactorTree 2 12

2 6

4 6

2 32 2

23 3 2

3 32 3


Take Out Your Study Guide!!!


FACTORFACTORA Factor is a number that is multipliedby another number to give the product.

7 x 8 = 56Factors

A Factor is the number that divides evenly into another number.

56 ÷ 8 = 7Factor

#3


Prime Numbers- A Prime number is a whole number with exactly 2 factors, one and itself.

Example: 17, 3, 2, 11, 13, 5

Composite Numbers- A Composite number is a number that has more than two factors.

Example: 9, 30, 64, 8, 40, 69

#4 Prime & Composite


Teacher Note: Use the next slide as a master. Make one

copy for each student to use to do this interactive lesson on

discovering prime 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

Hundreds Chart

http:// sieve of eratosthenes

Documents