1. Prime Numbers Eratosthenes’ SieveBy

2. Eratosthenes (ehr-uh-TAHS-thuh-neez)
Eratosthenes was the librarian at
Alexandria, Egypt in 200 B.C.

3. 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.

4. Eratosthenes’ Sieve
A sieve has holes in it and is used to filter out liquids from solids.
Eratosthenes’s sieve filters out numbers to find the prime numbers.

5. Definition
A Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors

6. Definition
A Factor – a number that divides exactly into another.
56 ÷ 8 = 7
Factor

7. 1 x 7 = 7 Definition 7 is prime because the only numbers
A Prime Number – a number that has only two factors, itself and 1.
1 x 7 = 7
7 is prime because the only numbers
that will divide into it evenly are 1 and 7.
Note: 1 is not a PRIME as it only has 1 factor repeated, 1x1 = 1

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

9. A 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

10. 1 – Cross out 1; it is not prime.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

11. Remember all numbers divisible by 2 are even numbers.
Hint For Next Step
Remember all numbers divisible by 2 are even numbers.

12. 2 – Leave 2; cross out multiples of 21 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

13. 2 6 7 Total of digits = 15 3 divides evenly into 15
Hint For Next Step
To 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 7
Total of digits = 15
3 divides evenly into 15
267 is a multiple of 3

14. 3– Leave 3; cross out multiples of 31 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

15. 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
& 890 is a multiple of 5
because the last digit
ends with 0 or 5.

16. 4– Leave 5; cross out multiples of 51 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

17. 5– Leave 7; cross out multiples of 71 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

18. 6–Leave 11; cross out multiples of 112 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

19. All the numbers left are prime1 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

20. 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