Sieve of Eratosthenes
copyright©amberpasillas2010
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 the Sieve of
Eratosthenes.
copyright©amberpasillas2010
1
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.
copyright©amberpasillas2010
FACTOR
A Factor is a number that is
multiplied by another number to
give the product.
7 x 8 = 56
Factors
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2
FACTOR
A Factor is the number that
divides evenly into another.
56 ÷ 8 = 7
Factor
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PRIME NUMBER
A Prime Number is 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©amberpasillas2010
3
Hundreds Chart
I am going to give you a hundreds
chart with the numbers from 1 to
100, with 10 numbers in each row.
You are going to use the Sieve of
Eratosthenes to discover the prime
numbers between 1 and 100.
copyright©amberpasillas2010
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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
4
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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
Hint For Next Step
Remember all numbers
divisible by 2 are even
numbers. Remember they
end in 0, 2, 4, 6, 8…
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5
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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
Hint For Next Step
To find multiples of 3, add the digits of
a number. If the sum divides evenly by
3 then the number is a multiple of 3.
267
Add the digits: 2 + 6 + 7 = 15
15 is divisible by 3 so
267 is a multiple of 3
copyright©amberpasillas2010
6
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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
Hint For the Next Step
Remember the number 4 is a
multiple of 2 and an even
number. You don’t have to do
multiples of 4 since you already
crossed off multiples of 2.
copyright©amberpasillas2010
7
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
and 890 is a multiple of 5
because the last digit
ends with 0 or 5.
copyright©amberpasillas2010
5 – 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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
8
Hint For the Next Step
Remember a number is
divisible by 6 if it is divisible
by 2 and 3. Since you have
already crossed out multiples
of 2 and 3 then you have
already done multiples of 6.
copyright©amberpasillas2010
7 – 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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
9
Hint For the Next Step
Remember 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?
copyright©amberpasillas2010
11 – 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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
copyright©amberpasillas2010
10
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
copyright©amberpasillas2010
Circle the rest of the primes on your 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©amberpasillas2010
11
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!
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
copyright©amberpasillas2010
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
24
Factor
2 12
4 6
Tree
2 6
2 2 2 3
2
3 23 • 3
23 • 3
copyright©amberpasillas2010
12
Take Out Your Study Guide!!!
copyright©amberpasillas2010
#3
FACTOR
A Factor is a number that is multiplied
by another number to give the product.
7 x 8 = 56
Factors
A Factor is the number that divides evenly
into another number.
56 ÷ 8 = 7
Factor
copyright©amberpasillas2010
13
#4
Prime & Composite
Prime NumbersA Prime number is a whole number
with exactly 2 factors, one and itself.
Example: 17, 3, 2, 11, 13, 5
Composite NumbersA Composite number is a number that
has more than two factors.
Example: 9, 30, 64, 8, 40, 69
copyright©amberpasillas2010
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
copyright©amberpasillas2010
14
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
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
15