Divisibility Rules Prime Factorization by jfo99047

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									 Divisibility Rules
         &
Prime Factorization

      Lesson 4-2
The standard you are working on
Number Sense 1.4 (grade 5)
  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
  understanding of sixth grade standard,
  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
Add up all the digits.
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
Add up all the digits.
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
      A video from YouTube
 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
A Random Thought about
    Prime Numbers

 Brought to you from YouTube.com

								
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