# Divisibility Rules Prime Factorization by jfo99047

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```									 Divisibility Rules
&
Prime Factorization

Lesson 4-2
The standard you are working on
Determine the prime factors of all numbers
through 50 and write the numbers as the
product of their prime factors by using
exponents to show multiples of a factor

You will be building upon this standard so
that you can successfully work toward the
Number Sense 2.4
The standard you are working toward

Number Sense 2.4
Determine the least common multiple and
the greatest common divisor of whole
numbers; use them to solve problems with
fractions (e.g., to find a common
denominator to add two fractions or to find
the reduced form for a fraction).
This lesson will be broken
into three parts
Prime vs. composite numbers
Divisibility rules
Prime factorization
Using divisibility rules to find prime factors
Using factor trees to find the prime
factorization of numbers
Putting prime factors into exponential form
as needed
Prime Numbers
vs.
Composite Numbers
Key Vocabulary
Factor
Prime number
Composite number
Factor
The numbers that are
multiplied to give a product
15 = 3 x 5
3 and 5 are factors of 15
Composite Number
Any factor that has at least 3
factors including one and itself
4:    1, 2, and 4
6:    1, 2, 3, and 6
9:    1, 3, and 9
10:   1, 2, 5, 10
Prime number
Any number who has only two
factors: one and itself

1 is not a prime number; it is a unit
Its only factor is 1

Examples of prime numbers
2, 3, 5, 7, 11
Using a 100 chart to find
prime numbers between
1 and 100…
Here is how…
2 is a prime number. All other multiples
of 2 are composite. Cross them off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99        100
3 is a prime number. All other multiples
of 3 are composite. Cross them off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99        100
5 is a prime number. All other multiples
of 5 are composite. Cross them off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99        100
7 is a prime number. All other multiples
of 7 are composite. Cross them off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99        100
Why did we skip 6?

The factors of 6 are 2 and 3. We
already crossed off all factors of
two and three.
11 is a prime number. All other multiples
of 11 are composite. Cross them off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99        100
13 is a prime number. All other multiples
of 13 are composite. Cross them off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99        100
17 is a prime number. All other multiples of 17
are composite. They are already crossed off.
1   2   3   4   5   6   7   8   9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99         100
Continue this process until all
prime numbers are circled and
all composite numbers are
crossed off.
All of the orange numbers on this chart are prime. Write them down.
Refer to them so you don’t waste time trying to factor them.

1    2    3    4    5    6    7    8    9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99                   100
A Rhyme to Help Us Remember

Prime number
Prime number
What do you see?
I see no other factors
Except for one and me.

Composite number
Composite number
What do you see?
I see at least three factors
Including one and me.
Divisibility Rules
The Rule for 2
If a number is even, then it is divisible by
two.
An even number is any number that ends in a
2, 4, 6, 8, or 0

93             76
52
98
100
The Rule for 3
If the sum of all digits is divisible by 3,
then the whole number is divisible by 3!
6321 = 6 + 3 + 2 + 1 =12
3 goes into 12 evenly, so 6321 is divisible by 3

63                                               28
981                21             762
The Rule for 4
The last two numbers are either 00 or
they are divisible by 4.
An even number is any number that ends in a
2, 4, 6, 8, or 0

804                                   217
724                       916
600
The Rule for 5
The number ends in a 5 or a zero.

93

90                   75
55                                  100
The Rule for 9
If the sum of all digits is divisible by 9,
then the whole number is divisible by 9!
6327 = 6 + 3 + 2 + 7 =18
9 goes into 18 evenly, so 6327 is divisible by 9

81                   312                        1125
414                        882
The Rule for 10
The number ends in a zero

9003
5840 6430
1020        70
Divisibility Rules Explained

1. Video from teachertube.com
2. Explanation from Mrs. Glosser
Let’s Practice…

Interactive Divisibility Rules Practice
Prime Factorization
Writing a number as a
product of its primes
Factor Trees
A video from TeacherTube.com
Interactive Practice for
Factor Trees
1. Virtual Manipulatives
2. Interactive Practice 1
3. Interactive Practice from MathPlayground.com
The Birthday Cake Method
a.k.a. The Box Method

An alternative to factor trees
Challenge Problem
Use what you know about multiplying
whole numbers by variables and
exponents to make a factor tree for the
following monomial
45x3
45    x3

9       5xx x
3       3