Prime Numbers

1
Discovering
Prime Numbers
Sieve of Eratosthenes
2
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.

3
Sieve of Eratosthenes
A sieve has holes in it and is used to filter
out the juice. Eratostheness sieve filters
out numbers to find the prime numbers.
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FACTOR

• A Factor is a number that is
• multiplied by another number to
• give the product.

7 x 8 56
Factors
5
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.
7
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.
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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
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1 Cross out 1 it is NOT prime.
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
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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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2 Leave 2 Cross out multiples of 2
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
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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.

2 6 7 Add the digits 2 6 7 15
15 is divisible by 3 so 267 is a multiple of 3
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3 Leave 3 Cross out multiples 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
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Hint For the Next Step
Remember the number 4 is a multiple of 2 and an
even number. You dont have to do multiples of 4
since you already crossed off multiples of 2.
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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.
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5 Leave 5 Cross out multiples of 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
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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.
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7 Leave 7 Cross out multiples of 7
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
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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?
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11 Leave 11 Cross out multiples of 11
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
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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
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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
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The Prime Numbers from 1 to 100 are as follows
Write these down on the bottom of your paper
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!
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
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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.
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24
Factor Tree
2
12
4
6
2
6
2
2
3
2
2
3
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That's all Folks!
Take Out Your Study Guide!!!
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FACTOR
3

• 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
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4 Prime Composite
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
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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
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Discovering Prime Numbers
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