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Prime and Composite Numbers

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**Vocabulary Product 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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**5 Vocabulary 5 is prime because the only numbers**

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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**All the numbers left are prime!**

4– Leave 5; cross out multiples of 5 2 – Leave 2; cross out multiples of 2 3– Leave 3; cross out multiples of 3 5– Leave 7; cross out multiples of 7 All the numbers left are prime! 1 – Cross out 1; it is not prime. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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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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**8 Vocabulary The factors of 8 are 1, 2, 4, 8**

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

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**Examples of Composite Numbers**

4, 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**

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. One is not a prime nor a composite number.

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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 2 x 3 = 12

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**How to Do Prime Factorization Using a Factor Tree**

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

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**There is More Than One Way…**

36 36 36 4 9 2 18 6 6 2 2 3 3 2 9 2 3 2 3 3 3 …but the prime factorization will always be the same. Prime Factorization 2 2 x 2 3 =36

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**How to Do Prime Factorization Using a Factor Tree**

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

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**How to Do Prime Factorization Using a Factor Tree**

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

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