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TEKS
®Chapter 111.17=
Mathematics Grade 5
®Item b - Knowledge and Skills
®(5.5) – Patterns, Relationships and Algebraic
Thinking
®The student makes generalizations based on observed
patterns and relationships
®c – Identify prime and composite numbers =
using
concrete models and patterns in factor pairs
<=
/div>
®
Objective
®The student w=
ill be
able to define, identify and determine the prime and composite
numbers up to 100. Determination
will be by means of a simple procedure.
Did you ever wonder?
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®What do the following sets of numbers have in common?
®4, 6, 8, 9, 12, 15
®
®2, 3, 5, 7, 11, 13
®
®Why can’t this number be in either set?
=
®1
®
![](3D"master168_background.gif")
![](3D"master168_image004.gif")
![](3D"master168_image005.jpg")
by Monica
Yuskaitis
Definition
® Product
– An answer to a multiplication problem.
7 x 8 =3D 56
Product
![](3D"slide0002_image006.gif")
Definition
® Factor
– a number that is multiplied
by another to give a pro=
duct.
7 x 8 =3D 56
Factors
![](3D"slide0003_image007.gif")
![](3D"slide0003_image008.gif")
Definition
® Factor
– a number that divi=
des
evenly into another.
56
÷ 8 =3D 7
Factor
![](3D"slide0004_image009.gif")
What are the factors?
6 x 7 =3D 42
7 x 9 =3D 63
8 x 6 =3D 48
4 x 9 =3D 36
6
& 7
7
& 9
8
& 6
4
& 9
What are the factors?
42 ÷ 7 =3D 6
63 ÷ 9 =3D 7
48 ÷ 6 =3D 8
36 ÷ 9 =3D 4
7
9
6
9
![](3D"slide0009_image010.gif")
Definition
® Prime Number
– a number that=
has
only two factors, itself and
1.
7
7 is prime because=
the
only numbers
that will divide i=
nto
it evenly are 1 and 7.
Examples of Prime Numbers
2, 3,
5, 7, 11, 13, 17, 19
![](3D"slide0011_image011.gif")
Special Note:
=
One is not a prime
number.
Definition
® Composite number – a number that has more than two factors.
8
The factors of 8 are 1, 2, 4, 8
Examples of Composite Numbers
4, 6,
8, 9, 10, 12, 14, 15
![](3D"slide0010_image012.gif")
Special Note:
=
Every whole number
from 2 on is
eit=
her
composite or prime.
Our
Lonely 1
![](3D"slide0008_image013.gif")
Special Note:
=
One is not a prime=
nor
a composite number=
.
![](3D"slide0008_image015.gif")
![](3D"slide0008_image016.gif")
It =
is
not prime
because it does
not
have exactly
two different
factors.
![](3D"slide0008_image017.gif")
It =
is
not
composite
bec=
ause
it does
not have more
than 2 factors.
![](3D"slide0008_image018.gif")
![](3D"slide0008_image019.gif")
![](3D"slide0008_image020.gif")
![](3D"slide0008_image021.gif")
Definition
® Prime Factorization – A way to write a composite number as the product of prime factors.
2 x 2 x 3 =3D 12
or
2 x 3 =3D
12
2
How to Do Prime Factorizatio=
n Using a Factor Tree
48
![](3D"slide0013_image022.gif")
Step 1 – Sta=
rt
with a composite number.
![](3D"slide0013_image023.gif")
Ste=
p 2
– Write down a multiplication
pro=
blem
that equals this number or
any
pair of factors of this number.
6 x 8 =3D 48
How to Do Prime Factorizatio=
n Using a Factor Tree
![](3D"slide0014_image024.gif")
Step 3 – Find
factors of these factors.
6 x 8
=3D 48
![](3D"slide0014_image025.gif")
![](3D"slide0014_image026.gif")
![](3D"slide0014_image027.gif")
![](3D"slide0014_image028.gif")
2 x 3 x 2 x 4 =3D 48
How to Do Prime Factorizatio=
n Using a Factor Tree
![](3D"slide0015_image029.gif")
=
Ste=
p 4
– Find factors of these numbers
unt=
il
all factors are prime numbers.
6 x 8
=3D 48
![](3D"slide0015_image030.gif")
2 x 3
x 2 x 4 =3D 48
![](3D"slide0015_image031.gif")
![](3D"slide0015_image032.gif")
2 x 3 x 2 x 2 x 2 =3D 48
How to Do Prime Factorizatio=
n Using a Factor Tree
![](3D"slide0016_image033.gif")
=
Ste=
p 5
– Write the numbers from least
to greatest.
6 x 8
=3D 48
2 x 3
x 2 x 2 x 2 =3D 48
2 x 2 x 2 x 2 x 3 =3D 48
How to Do Prime Factorizatio=
n Using a Factor Tree
![](3D"slide0017_image034.gif")
=
Step 6 – Count how many numbers are
the
same and write exponents for them.
6 x 8
=3D 48
2 x 3
x 2 x 2 x 2 =3D 48
2 x 2 x 2 x 2 x 3 =3D 48
2 x 3
=3D 48
4
![](3D"slide0017_image035.gif")
![](3D"slide0017_image036.gif")
![](3D"slide0017_image037.gif")
![](3D"slide0017_image038.gif")
Prime factor this number
4
![](3D"slide0018_image039.gif")
![](3D"slide0018_image040.gif")
2 x 2
2 =3D 4
2
=3D 4
![](3D"slide0018_image041.gif")
![](3D"slide0018_image042.gif")
Prime factor this number
6
![](3D"slide0019_image043.gif")
![](3D"slide0019_image044.gif")
2 x 3
=3D 6
Prime factor this number
8
![](3D"slide0023_image045.gif")
![](3D"slide0023_image046.gif")
2 x 4
2 =3D 8
3
=3D 8
![](3D"slide0023_image047.gif")
![](3D"slide0023_image048.gif")
2 x 2
x 2 =3D 8
![](3D"slide0023_image049.gif")
![](3D"slide0023_image050.gif")
![](3D"slide0023_image051.gif")
Prime factor this number
9
![](3D"slide0021_image052.gif")
![](3D"slide0021_image053.gif")
3 x 3
=3D 9
3 =3D 9
2
![](3D"slide0021_image054.gif")
![](3D"slide0021_image055.gif")
Prime factor this number
10
![](3D"slide0022_image056.gif")
![](3D"slide0022_image057.gif")
2 x 5
=3D 10
Prime factor this number
12
![](3D"slide0020_image058.gif")
![](3D"slide0020_image059.gif")
3 x 4
2 x 3 =3D 12
2
=3D 12
![](3D"slide0020_image060.gif")
![](3D"slide0020_image061.gif")
3 x 2
x 2 =3D 12
2 x 2
x 3 =3D 12
![](3D"slide0020_image062.gif")
![](3D"slide0020_image063.gif")
Prime factor this number
14
![](3D"slide0024_image064.gif")
![](3D"slide0024_image065.gif")
2 x 7
=3D 14
Prime factor this number
15
![](3D"slide0025_image066.gif")
![](3D"slide0025_image067.gif")
3 x 5
=3D 15
Prime factor this number
16
![](3D"slide0027_image068.gif")
![](3D"slide0027_image069.gif")
4 x 4
2 =3D 16
4
=3D 16
![](3D"slide0027_image070.gif")
![](3D"slide0027_image071.gif")
2 x 2
x 2 x 2 =3D 16
![](3D"slide0027_image072.gif")
![](3D"slide0027_image073.gif")
![](3D"slide0027_image074.gif")
![](3D"slide0027_image075.gif")
![](3D"slide0027_image076.gif")
![](3D"slide0027_image077.gif")
Prime factor this number
18
![](3D"slide0028_image078.gif")
![](3D"slide0028_image079.gif")
3 x 6
2 x
3 =3D 18
2
=3D 18
![](3D"slide0028_image080.gif")
![](3D"slide0028_image081.gif")
3 x 2
x 3 =3D 18
![](3D"slide0028_image082.gif")
2 x 3
x 3 =3D 18
![](3D"slide0028_image083.gif")
Prime factor this number
20
![](3D"slide0029_image084.gif")
![](3D"slide0029_image085.gif")
4 x 5
2 x 5 =3D 20
2
=3D 20
![](3D"slide0029_image086.gif")
![](3D"slide0029_image087.gif")
2 x 2
x 5 =3D 20
![](3D"slide0029_image088.gif")
![](3D"slide0029_image089.gif")
Prime factor this number
21
![](3D"slide0026_image090.gif")
![](3D"slide0026_image091.gif")
3 x 7
=3D 21
Prime factor this number
22
![](3D"slide0030_image092.gif")
![](3D"slide0030_image093.gif")
2 x
11
=3D 22
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