5th grade Lesson PPT Factorization 12 18 08 - PowerPoint

							 Factorization
Greatest Common Factor
 Least Common Multiple
             Why Factor?
 Factors allow you to break composite
  numbers down to their component parts.
 Factors are used to simplify fractions.
 Factors are used to identify the greatest
  common factor (GCF) and the least
  common multiple (LCM).
 A number can be written as the product of
  its prime factors.
      Find Factor Pairs for 24
 Start with 1: 1 x 24 = 24
 2: 2 x 12 = 24
 3: 3 x 8 = 24               The commutative
                              property shows the
 4: 4 x 6 = 24               same pairs:
 6: 6 x 4 = 24               1 x 24 = 24 x 1
                              2 x 12 = 12 x 2
 8: 8 x 3 = 24               3x8=8x3
                              4x6=6x4
 12: 12 x 2 = 24
 24: 24 x 1 = 24
        Prime Factorization
 Prime numbers are numbers that have
  only one and the number as factors.
 “1” is neither prime or composite.
 Composite numbers can be written as
  products of their prime factors.
Factorization
Upside Down Division
    Prime factorization of 24

              2 24
              2 12
              2 6
                 3
Prime Factorization is 2 x 2 x 2 x 3
    Prime factorization of 28

              2 28
              2 14
                 7

Prime Factorization is 2 x 2 x 7
    Prime factorization of 15

              3 15
                 5

Prime Factorization is 3 x 5
         Prime factor 40

              2 40
              2 20
              2 10
                 5
Prime Factorization is 2 x 2 x 2 x 5
Greatest Common Factor (GCF)
   Definition:
    – The largest factor that divides evenly into 2 or
      more numbers.


   Examples:
    – 3 and 7 have no common factors other than 1
    – 4 and 6 have the greatest common factor of 2
    – 6 and 24 have a greatest common factor of 6
    – 10 and 15 have a GCF of 5
Greatest Common Factor
      Use Factorization
     Prime factor 28 and 16
         to find the GCF
      2 28            2 16
      2 14             2 8
          7           2 4
                          2
Prime Factorization   Prime Factorization
  of 28: 2 x 2 x 7    of 16: 2 x 2 x 2 x 2
     Prime factor 28 and 16

       2 28                2 16
       2 14                2 8
          7                2 4
                              2
Prime Factorization   Prime Factorization
  of 28: 2 x 2 x 7    of 16: 2 x 2 x 2 x 2
Factor both numbers 28 and 16
       at the same time
   2 28     16
   2 14      8
      7      4

   The GCF is the product of the
   common prime factors: 2 x 2 = 4
Factor both numbers: 24 and 30

    2 24     30
    3 12     15
       4      5

    The GCF is the product of the
    common prime factors: 2 x 3 = 6
Factor both numbers: 28 and 42


 G  2 28
    7 14
       2
             42
             21
              3

    The GCF is the product of the
    common prime factors: 2 x 7 = 14
Factor both numbers: 12 and 30


  G 2 12
    3 6
       2
             30
             15
              5

    The GCF is the product of the
    common prime factors: 2 x 3 = 6
Least Common Multiple
     Use Factorization
Factor both numbers 28 and 16
       at the same time
   2 28      16
   2 14       8
      7       4

   The LCM is the product of ALL the
   factors: 2 x 2 x 7 x 4 = 112
Factor both numbers: 24 and 30

    2 24      30
    3 12      15
       4       5

    The LCM is the product of ALL of
    the factors: 2 x 3 x 4 x 5 = 120
Factor both numbers: 28 and 42

    2 28      42
    7 14      21
       2       3

    The LCM is the product of ALL of
    the factors: 2 x 7 x 2 x 3 = 84
Factor both numbers: 12 and 30

    2 12      30
    3 6       15
       2       5

    The LCM is the product of ALL of
    the factors: 2 x 3 x 2 x 5 = 60
Greatest Common Factor
          and
 Least Common Multiple
Factor both numbers: 10 and 30


 G  5 10
    2 2
       1
              30
               6
               3

    GCF: 5 x 2 = 10
    LCM: 5 x 2 x 1 x 3 = 30
Factor both numbers: 12 and 40


 G  2 12
    2 6
       3
              40
              20
              10

    GCF: 2 x 2 = 4
    LCM: 2 x 2 x 3 x 10 = 120
Factor both numbers: 12 and 40


 G  2 12
    2 6
       3
              40
              20
              10

    GCF: 2 x 2 = 4
    LCM: 2 x 2 x 3 x 10 = 120
Simplifying Fractions
  Greatest Common Factor
       Simplify 24/30

2 24          30
3 12          15
   4           5

The fraction 24/30
simplifies to 4/5
(The GCF was used: 24/6 = 4, 30/6 = 5)
       Simplify 28/42

2 28          42
7 14          21
   2           3

The fraction 28/42
simplifies to 2/3
(The GCF was used: 28/14 = 2, 42/14 = 3)
       Simplify 12/40

2 12          40
2 6           20
   3          10

The fraction 12/40
simplifies to 3/10
(The GCF was used: 12/4 = 3, 40/4 = 10)