7 Eratosthenes (ehr-uh-TAHS-thuh-neez) Eratosthenes was a librarian fromAlexandria, Egypt in 200 B.C.ENote: every book was a scroll.
8 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.
9 Eratosthenes’ SieveA sieve has holes in it and is used to filter out the liquid.Eratosthenes’s sieve filters out numbers to find the prime numbers.
10 Hundreds ChartOn graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.
11 All the numbers left are prime! 4– Leave 5; cross out multiples of 52 – Leave 2; cross out multiples of 23– Leave 3; cross out multiples of 35– Leave 7; cross out multiples of 7All the numbers left are prime!1 – Cross out 1; it is not prime.123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
12 The 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
14 8 Vocabulary The factors of 8 are 1, 2, 4, 8 Composite number – a number that has more than two factors.8The factors of 8 are 1, 2, 4, 8
15 Examples of Composite Numbers 4, 6, 8, 9, 10, 12, 14, 15Special Note:Every whole number from 2 on iseither composite or prime.
16 1 is the Loneliest Number It is not primebecause it doesnot have exactlytwo differentfactors.It is notcompositebecause it doesnot have morethan 2 factors.One is not a prime nora composite number.
17 DefinitionPrime Factorization – A way to write a composite number as the product of prime factors.2 x 2 x 3 = 12or22 x 3 = 12
18 How to Do Prime Factorization Using a Factor Tree Step 1: Begin with a composite number.36Step 2: Find two factors that can be multiplied to make that number492323=36xxxStep 3: continue finding factors until all are prime.Prime Factorization222x3= 36Step 4: rewrite using exponents.
19 There is More Than One Way… 3636364921866223329232333…but the prime factorization will always be the same.Prime Factorization22x23=36
20 How to Do Prime Factorization Using a Factor Tree Step 1: Begin with a composite number.54Step 2: Find two factors that can be multiplied to make that number69x2xx33=543Step 3: continue finding factors until all are prime.Prime Factorization32x3= 54Step 4: rewrite using exponents.
21 How to Do Prime Factorization Using a Factor Tree Step 1: Begin with a composite number.48Step 2: Find two factors that can be multiplied to make that number684232Step 3: continue finding factors until all are prime.Prime Factorization4x223=482Step 4: rewrite using exponents.
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