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Vocabulary Product – An answer to a multiplication problem. 7 x 8 = 56 Product

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

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Vocabulary Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

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Vocabulary Prime Number – a number that has only two factors, 1 and itself. 5 5 is prime because the only numbers that will divide into it evenly are 1 and 5.

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Prime Numbers: Eratosthenes’s Sieve

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Eratosthenes (ehr-uh-TAHS-thuh-neez) Eratosthenes was a librarian from Alexandria, Egypt in 200 B.C.E Note: every book was a scroll.

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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.

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

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

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100999897969594939291 90898887868584838281 80797877767574737271 70696867666564636261 60595857565554535251 50494847464544434241 40393837363534333231 30292827262524232221 20191817161514131211 10987654321 1 – Cross out 1; it is not prime. 2 – Leave 2; cross out multiples of 2 3– Leave 3; cross out multiples of 3 4– Leave 5; cross out multiples of 5 5– Leave 7; cross out multiples of 7 All the numbers left are prime!

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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

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Factors, Primes, & Composite Numbers

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Vocabulary Composite number – a that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8

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Examples of Composite Numbers 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

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1 is the Loneliest Number One is not a prime nor a composite number. It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors.

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Definition Prime Factorization – A way to write a composite number as the product of prime factors. 2 x 2 x 3 = 12 or 2 x 3 = 12 2

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How to Do Prime Factorization Using a Factor Tree Step 1: Begin with a composite number. Step 2: Find two factors that can be multiplied to make that number Step 3: continue finding factors until all are prime. 36 4 9 2 2 3 3 Step 4: rewrite using exponents. x x =36 23 x 22 = 36 x Prime Factorization

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There is More Than One Way… 2 3 36 4 9 2 3 23 x 22 =36 Prime Factorization 3 2 36 2 18 3 9 3 2 36 6 6 2 3 …but the prime factorization will always be the same.

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How to Do Prime Factorization Using a Factor Tree Step 1: Begin with a composite number. Step 2: Find two factors that can be multiplied to make that number Step 3: continue finding factors until all are prime. 54 6 9 2 3 3 3 Step 4: rewrite using exponents. x x =54 23 x 3 = 54 x Prime Factorization

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How to Do Prime Factorization Using a Factor Tree Step 1: Begin with a composite number. Step 2: Find two factors that can be multiplied to make that number Step 3: continue finding factors until all are prime. 48 6 8 2 3 2 2 2 Step 4: rewrite using exponents. 23 x 4 =48 4 Prime Factorization

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