Transcript Factors and Prime Factorization

Do Now 1/31/11
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Take out HW from Tuesday night.
– “The Sieve of Eratosthenes”
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Copy HW in your planner.
– Text page 175, #16-44 evens
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Be ready to copy POTW #2
Homework
The “Sieve of Eratosthenes”
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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.
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2) Removing multiples removes
composite numbers, which leaves only
primes.
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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
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SWBAT write the prime factorization of a
number
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SWBAT write the prime factorization of a
monomial
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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
7
6
Prime
1
2
Neither
8
5
3
Composite
Factoring Natural Numbers
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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.
divisor
– Example:
39 ÷ 3 = 13
quotient
dividend
3 · 13 = 39
factor
factor
product
Factoring Natural Numbers
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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
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Write the prime factorization of the following numbers using
tree diagrams.
40
225
5 ∙ 8
5 ∙ 45
5 ∙ 2 ∙ 4
**HINT
Write your factors
in increasing order.
5 ∙ 3 ∙ 3 ∙ 5
5 ∙ 2 ∙ 2 ∙ 2
3 ∙ 3 ∙ 5 ∙ 5
2 ∙ 2 ∙ 2 ∙ 5
2³ ∙ 5
5 ∙ 3 ∙ 15
When you have repeating
factors use exponents.
3² ∙ 5²
Monomial
a number, a variable, or the product of a
number and one or more variables with whole
number exponents
7
x
3x³yz²
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
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Factor each monomial.
6ab
63a³
=2·3·a·b
=3·3·7·a·a·a
18x²y
=2·3·3·x·x·y
36s³t²
=2·2·3·3·s·s·s·t·t
What Did We Learn Today?
24
-7
-4
-5
8
Homework
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Text page 175, #16-44 multiples of 4;
#48-54 evens