Presentation Transcript
Prime NumbersEratosthenes’ Sieve: Prime Numbers Eratosthenes’ Sieve By Monica Yuskaitis
Eratosthenes(ehr-uh-TAHS-thuh-neez): Eratosthenes (ehr-uh-TAHS-thuh-neez) Eratosthenes was the librarian at
Alexandria, Egypt in 200 B.C.
Note every book was a scroll.
Eratosthenes(ehr-uh-TAHS-thuh-neez): 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.
Eratosthenes’ Sieve: Eratosthenes’ Sieve 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.
Definition: Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors
Definition: Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor
Definition: Definition Prime Number – 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.
Hundreds Chart: Hundreds Chart On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.
Slide9: Hundreds Chart
Slide10: 1 – Cross out 1; it is not prime.
Hint For Next Step: Hint For Next Step Remember all numbers divisible by 2 are even numbers.
Slide12: 2 – Leave 2; cross out multiples of 2
Hint For Next Step: 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
Slide14: 3– Leave 3; cross out multiples of 3
Slide15: 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 5
andamp; 890 is a multiple of 5
because the last digit
ends with 0 or 5.
Slide16: 4– Leave 5; cross out multiples of 5
Slide17: 5– Leave 7; cross out multiples of 7
Slide18: 6–Leave 11; cross out multiples of 11
Slide19: All the numbers left are prime
The Prime Numbers from 1 to 100 are as follows:: 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
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