Transcript Prime Factorization

Factors and Prime Factors
5.2
What Will We Accomplish?
• After reviewing the characteristics of prime
and composite numbers . . . .
We will write the prime factorization of
composite numbers.
We will look at this skill in three ways. The
“Think Box” method will be the most useful in
future math classes.
Prime or Composite Review
• It is helpful to identify a number as prime or
composite when trying to simplify a value.
• Prime numbers have only two factors: Itself
and the number 1.
• The number “1” is neither prime nor
composite. It has only one factor.
• The number 2 is the only even number that is
prime.
Factors are multiplication “facts.”
Factors: whole numbers that are multiplied
together to form a product
Prime factorization: writing a product using
ONLY PRIME NUMBERS as a multiplication
problem.
8 = 2 x 2 x 2 = 23
Prime Factorization
Method 1: Factor Trees
Start with the composite number, and break it into two of its
factors.
4
The prime factors are 2∙2∙2∙3∙2= 2 ∙ 3
48
6
0
2
X
X
0
0
3
2
48
8
4
X
X
12
2
4
0
0
0
0
00
2
0
X
6 X
3 X2
2
2
x 2
Prime Factorization: Factor Tree Practice
Start with the composite number, and break it into two of its
factors.
50
30
3
0
3
x
x
0
5
10
0 0
2
2 x 3 x 5
x
5
90
9 x 10
x
10
0 0
5
x
2 x 5 x 5 = 2 x 52
2
0 000
3 x 3
2 x 5
2 x 5 x 3 x 3 = 2 x 32 x 5
Remember Our Objective!
• We are rewriting composite numbers as prime
factors.
• This means we are writing multiplication
problems that ONLY have prime factors in
them!
Prime Factorization: Method 2
Division Ladders
When using a division ladder, use only primes to divide.
2 48
2 24
2 12
2
6
3
These are your prime factors:
2x2x2x2x3
Add this to your notes.
3
30
2
10
5
The prime factors are 2 x 3 x 5
Prime Factorization: Division Ladder Practice
Remember, use only primes to divide.
2 100
2 50
5 25
5
2x2x5x5=
22 x 52
5 250
5 50
5 10
2
5 x 5 x 5 x 2 = 2 x 53
Prime Factorization: Method 3
Think Box
Primes
This is a new method. This is the method that will help you with the
rest of the chapter and into next year. It is shown in a different form in your text.
48 =
6x 8 =
3 x 2 x2x2x2
Make a “think box” to organize your thoughts.
List two factors that = 48.
Take one factor at a time and break it into prime factors.
Remembering that 8 = 2 x 2 x 2 will save you a tremendous amount of time!
90 =
9 x 10 =
3 x 3x 2 x 5
2 x 32 x 5
Think Box Practice
120 = 12 x 10 =
66 =
6 x 11 =
23 x 3 x 5
2 x 2 x 3 x 2 x 5
2 x 3 x 11
23 x 11=
88 = 8 x 11 = 2 x 2 x 2 x 11
Remember the 8!!!!
36 = 6 x 6 =
45 = 5 x 9 =
2 2 x 32
2 x 3 x 2 x 3
5 x 3 x 3
5 x 32
1500 = 15 x 100 = 3 x 5 x 2 x 5 x 2 x 5
2 x5x2x 5
3 x 22 x 5 3
Have We Met Our Objective?
• Did we write composite numbers in the form
of prime factorizations?
• Did you find one method you preferred over
the others?
• Remember, you do not always have to use one
method. You can use a method that works
best for a specific problem.
• However….which one will be the most help in
future math classes?
Think in terms of primes.
Speed limits?
7x2x5
Ages? 2 x 2 x 3
Grades? 2 x 5 x 2 x 5
PRIMES