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**Do Now 1/31/11 Take out HW from Tuesday night.**

“The Sieve of Eratosthenes” Copy HW in your planner. Text page 175, #16-44 evens Be ready to copy POTW #2

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**Homework The “Sieve of Eratosthenes”**

1) 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; yes; these numbers only have two factors 1 and itself. 2) Removing multiples removes composite numbers, which leaves only primes. 3) 10 numbers; 101, 103, 107, 109, 113, 127, 131, 137, 139, 149

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**Chapter 4 “Factors, Fractions, and Exponents”**

Section 4.1 “Factors and Prime Factorization” Section 4.2 “Greatest Common Factor” Section 4.3 “Equivalent Fractions” Section 4.4 “Least Common Multiple”

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**Objective SWBAT write the prime factorization of a number**

SWBAT write the prime factorization of a monomial In your journal, answer the question below using the following definition. A factor of a number is a number that can be divided into the given number without a remainder. Which number do you think has more factors 24 or 29? Why? (Hint: List all of the factors of the number 24 and 29)

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**Section 4.1 “Factors and Prime Factorization”**

Natural numbers are classified according to how many factors they have: (1) Prime numbers: -a whole number that is greater than 1 and has exactly TWO factors, itself and 1. (2) Composite numbers: -a whole number that is greater than 1 and has more than two factors. (3) The number 1: 1 is neither prime nor composite.

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“Prime or Composite?” 4 1 Neither 5 7 2 6 8 3 Prime Composite

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**Factoring Natural Numbers**

A natural number is FACTORED when it is written as the product of two or more numbers. You can use divisibility tests to find factors of numbers. Example: ÷ 3 = 13 3 · 13 = 39 divisor quotient dividend product factor factor

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**Factoring Natural Numbers**

You can use TREE DIAGRAMS to factor a number until all factors are primes. 30 30 30 3 ∙ 10 2 ∙ 15 5 ∙ 6 3 ∙ 2 ∙ 5 2 ∙ 3 ∙ 5 5 ∙ 2 ∙ 3 **HINT Write your factors in increasing order. Prime Factorization -writing a number as a product of prime factors.

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**Factoring Natural Numbers**

Write the prime factorization of the following numbers using tree diagrams. 225 40 5 ∙ 45 5 ∙ 8 **HINT Write your factors in increasing order. 5 ∙ 3 ∙ 15 5 ∙ 2 ∙ 4 5 ∙ 3 ∙ 3 ∙ 5 5 ∙ 2 ∙ 2 ∙ 2 3 ∙ 3 ∙ 5 ∙ 5 2 ∙ 2 ∙ 2 ∙ 5 When you have repeating factors use exponents. 2 ∙ 5 3 ∙ 5

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**x 3x³yz² 7 3a³ = 3 · a · a · a Monomial a number, a variable,**

or the product of a number and one or more variables with whole number exponents x 3x³yz² 7 To FACTOR a monomial, write the monomial as a product of prime numbers and variables with exponents of 1. 3a³ = 3 · a · a · a

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**Factoring Algebraic Expressions**

Factor each monomial. 6ab 63a³ = 2 · 3 · a · b = 3 · 3 · 7 · a · a · a 18x²y 36s³t² = 2 · 3 · 3 · x · x · y = 2 · 2 · 3 · 3 · s · s · s · t · t

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What Did We Learn Today?

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**24 Homework Text page 175, #16-44 multiples of 4; #48-54 evens -7 -4**

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