Prime Numbers With Mrs Ford. Eratosthenes (ehr-uh-TAHS-thuh-neez) Eratosthenes was the librarian at...
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Transcript of Prime Numbers With Mrs Ford. Eratosthenes (ehr-uh-TAHS-thuh-neez) Eratosthenes was the librarian at...
Prime Prime NumbersNumbers
With Mrs FordWith Mrs Ford
EratosthenesEratosthenes(ehr-uh-TAHS-thuh-(ehr-uh-TAHS-thuh-neez)neez)
Eratosthenes was the librarian at Alexandria, Egypt in 200 B.C.
Note every book was a scroll.
EratosthenesEratosthenes(ehr-uh-TAHS-thuh-(ehr-uh-TAHS-thuh-neez)neez)
Eratosthenes was a GreekEratosthenes was a Greekmathematician, astronomer, mathematician, astronomer, and geographer.and geographer.He invented a method for He invented a method for finding prime numbers that finding prime numbers that is still used today.is still used today.
This method is called Eratosthenes’This method is called Eratosthenes’Sieve.Sieve.
Eratosthenes’ SieveEratosthenes’ Sieve
A sieve has holes in it A sieve has holes in it and is used to filter and is used to filter out the juice.out the juice.
Eratosthenes’s sieve Eratosthenes’s sieve filters out numbers filters out numbers to find the prime numbers.to find the prime numbers.
DefinitionDefinition
FactorFactor – a number that is – a number that is multiplied by another to give a multiplied by another to give a product.product.
7 x 8 = 56
Factors
DefinitionDefinition
FactorFactor – a number that – a number that divides evenly into another.divides evenly into another.
56 ÷ 8 = 7
Factor
DefinitionDefinition
Prime NumberPrime Number – a number that – a number that has only two factors, itself and 1.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 ChartHundreds Chart
On graph paper, make a chart of On graph paper, make a chart of the numbers from 1 to 100, with the numbers from 1 to 100, with 10 numbers in each row.10 numbers in each row.
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
Hundreds Chart
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
1 – Cross out 1; it is not prime.
Hint For Next StepHint For Next Step
Remember all numbers Remember all numbers divisible by 2 are divisible by 2 are even numbers.even numbers.
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
2 – Leave 2; cross out multiples of 2
Hint For Next StepHint For Next Step
To find multiples of 3, add the To find multiples of 3, add the digits of a number; see if you can digits of a number; see if you can divide this number evenly by 3; divide this number evenly by 3; then the number is a multiple of 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
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
3– Leave 3; cross out multiples of 3
To find the multiples of 5 look To find the multiples of 5 look for numbers that end with the for numbers that end with the digit 0 and 5.digit 0 and 5.
Hint For the Next Step
385 is a multiple of 5 & 890 is a multiple of 5 because the last digit
ends with 0 or 5.
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
4– Leave 5; cross out multiples of 5
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
5– Leave 7; cross out multiples of 7
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
6–Leave 11; cross out multiples of 11
11 22 33 44 55 66 77 88 99 1010
1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
3131 3232 3333 3434 3535 3636 3737 3838 3939 4040
4141 4242 4343 4444 4545 4646 4747 4848 4949 5050
5151 5252 5353 5454 5555 5656 5757 5858 5959 6060
6161 6262 6363 6464 6565 6666 6767 6868 6969 7070
7171 7272 7373 7474 7575 7676 7777 7878 7979 8080
8181 8282 8383 8484 8585 8686 8787 8888 8989 9090
9191 9292 9393 9494 9595 9696 9797 9898 9999 100100
All the numbers left are prime
The Prime Numbers The Prime Numbers from 1 to 100 are as from 1 to 100 are as follows: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
THE ENDTHE END
