Download Factors and Prime Factors

Factors and Prime Factors
What Will We Accomplish?
• We have reviewed the characteristics of prime
and composite numbers . . . .
• Today 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 two distinct 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
products of 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. These are written
outside of the division.
2 48
2 24
2 12
2
6
3
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.
48 =
6x 8 =
3 x 2 x2x2x2
Make a “think box” to organize your thoughts.
List two factors that have a product of 48.
Take one factor at a time and mentally 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
15 x 6 =
3 x 5x 2 x 3
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