Transcript Factors and Prime Factorization

Do Now 11/30/09
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Copy HW in your planner.
– Text page 175, #16-44 multiples of 4; #48-54 evens
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Be ready to copy POTW #3
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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)
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”
Section 4.5 “Rules of Exponents”
Section 4.6 “Negative and Zero Exponents”
Section 4.7 “Scientific Notation”
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
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
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