Eratosthenes was a Greek mathematician who invented a method for finding prime numbers called Eratosthenes' Sieve. The sieve works by starting with a list of consecutive numbers and systematically eliminating multiples of each prime number to discover the remaining prime numbers. It involves crossing out multiples of 2 first, then multiples of 3, and continuing for higher prime numbers, leaving only the prime numbers at the end. The document then demonstrates how to use Eratosthenes' Sieve to find all the prime numbers between 1 and 100.

1. Prime NumbersEratosthenes’ SieveBy Monica Yuskaitis

2. Copyright © 2000 by Monica YuskaitisEratosthenes(ehr-uh-TAHS-thuh-neez)Eratosthenes was the librarian at Alexandria, Egypt in 200 B.C. Note every book was a scroll.

3. Copyright © 2000 by Monica YuskaitisEratosthenes(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. Copyright © 2000 by Monica YuskaitisEratosthenes’ SieveA sieve has holes in it and is used to filter out the juice.Eratosthenes’s sieve filters out numbers to find the prime numbers.

5. Copyright © 2000 by Monica YuskaitisDefinitionFactor – a number that is multiplied by another to give a product.7 x 8 = 56Factors

6. Copyright © 2000 by Monica YuskaitisDefinitionFactor – a number that divides evenly into another.56 ÷ 8 = 7Factor

7. Copyright © 2000 by Monica YuskaitisDefinitionPrime Number – a number that has only two factors, itself and 1.77 is prime because the only numbersthat will divide into it evenly are 1 and 7.

8. Copyright © 2000 by Monica YuskaitisHundreds ChartOn graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.

9. Copyright © 2000 by Monica YuskaitisHundreds Chart

10. Copyright © 2000 by Monica Yuskaitis1 – Cross out 1; it is not prime.

11. Copyright © 2000 by Monica YuskaitisHint For Next Step Remember all numbers divisible by 2 are even numbers.

12. Copyright © 2000 by Monica Yuskaitis2 – Leave 2; cross out multiples of 2

13. Copyright © 2000 by Monica YuskaitisHint For Next StepTo 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 7Total of digits = 153 divides evenly into 15267 is a multiple of 3

14. Copyright © 2000 by Monica Yuskaitis3– Leave 3; cross out multiples of 3

15. Copyright © 2000 by Monica YuskaitisHint For the Next StepTo 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 5because the last digitends with 0 or 5.

16. Copyright © 2000 by Monica Yuskaitis4– Leave 5; cross out multiples of 5

17. Copyright © 2000 by Monica Yuskaitis5– Leave 7; cross out multiples of 7

18. Copyright © 2000 by Monica Yuskaitis6–Leave 11; cross out multiples of 11

19. Copyright © 2000 by Monica YuskaitisAll the numbers left are prime

20. Copyright © 2000 by Monica YuskaitisThe Prime Numbers from 1 to 100 are as follows: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

21. Copyright © 2000 by Monica YuskaitisCreditsClipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/clipgallerylive/default.asp