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

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

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”

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)

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.

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

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: 39 ÷ 3 = 13 3 · 13 = 39 divisor quotient dividend product factor factor

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.

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. ³ ² ² 2 ∙ 5 3 ∙ 5

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

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

What Did We Learn Today?

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