1. 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

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

3. 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”

4. 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)

5. 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.

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

7. 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

8. 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.

9. 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

10. 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

11. 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

12. What Did We Learn Today?

13. 24 Homework Text page 175, #16-44 multiples of 4; #48-54 evens -7 -4