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------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/master19.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADwQAAAAUAHAAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABAAAAC0BAAAEAAAAJwH//xwAAAD7 Avn/AAAAAAAAkAEAAAAAAEAAAFRhaG9tYQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAC0B AwAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAhYAAAAyCgoAPgAKAAAAVGhlIEJhc2ljcwQABAAE AAIABAAEAAMAAgADAAMABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAA AAAAAAAAGAAAAAEAAABwNxUA5AQAAAQAAAAtAQQABAAAAPABAwADAAAAAAA= ------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and they are used to tracked whole items.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>we say x is a multiple of y
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>we say x is a multiple of y or y is a factor<= /span> of x.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a = multiple of 3 (or 5),
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a = multiple of 3 (or 5), and 3 (or 5) is a factor of 15.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>by 1 and itself.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only. <= /span>
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0079.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime= .)
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
Example A: List the factors and the multiples = of 12.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
Example A: List the factors and the multiples = of 12.
The factors of 12: 1, 2, 3, 4, 6, and 12.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
Example A: List the factors and the multiples = of 12.
The factors of 12: 1, 2, 3, 4, 6, and 12. =
The multiples of 12: 12=3D1x12,
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
Example A: List the factors and the multiples = of 12.
The factors of 12: 1, 2, 3, 4, 6, and 12. =
The multiples of 12: 12=3D1x12, 24=3D2x12,
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
Example A: List the factors and the multiples = of 12.
The factors of 12: 1, 2, 3, 4, 6, and 12. =
The multiples of 12: 12=3D1x12, 24=3D2x12, 36=3D3x12, 48, 60, etc…
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Whole numbers 1, 2, 3, 4,.. are called natural numbers and = they are used to tracked whole items.
If x and y are two natural numbers and x can be divided by y, = we say x is a multiple of y or y is a factor<= /span> of x. Hence 15 is a multiple of 3 (or 5), and 3 (or 5) is a factor of 15. Note that a <= /span>number x is always the multiple of itself and the number 1.
A prime number is a natural number that can only be divided = by 1 and itself. Its factors consist of 1 and itself only.
Hence 2, 3, 5, 7, 11, 13,… are prime numbers. (1 is not prime.)
15 is not a prime number because 15 can be divided by 3 or 5.
Example A: List the factors and the multiples = of 12.
The factors of 12: 1, 2, 3, 4, 6, and 12. =
The multiples of 12: 12=3D1x12, 24=3D2x12, 36=3D3x12, 48, 60, etc…
Your turn: List the factors and multiple of 18= .
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely,
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0100.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
We write x*x*x…*x as xN where N is the number of x’s= = multiplied to itself.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
We write x*x*x…*x as xN where N is the number of x’s= multiplied to itself. N is called the exponent, or the power of x. <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>Hence, factored completely, 12 =3D 2*2*3 =3D 22*3.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0102.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
Example B:
 
32 
43
We write x*x*x…*x as xN where N is the number of x’s= multiplied to itself. N is called the exponent, or the power of x. <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>Hence, factored completely, 12 =3D 2*2*3 =3D 22*3.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0103.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
Example B:
 
32 =3D 3*3 =3D 9        = ;          
43
We write x*x*x…*x as xN where N is the number of x’s= multiplied to itself. N is called the exponent, or the power of x. <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>Hence, factored completely, 12 =3D 2*2*3 =3D 22*3.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
Example B:
 
32 =3D 3*3 =3D 9        = ;           (note that 3*2 =3D 6)
43
We write x*x*x…*x as xN where N is the number of x’s= multiplied to itself. N is called the exponent, or the power of x. <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>Hence, factored completely, 12 =3D 2*2*3 =3D 22*3.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
Example B:
 
32 =3D 3*3 =3D 9        = ;           (note that 3*2 =3D 6)
43 =3D 4*4*4 =3D 64        = ;      
We write x*x*x…*x as xN where N is the number of x’s= multiplied to itself. N is called the exponent, or the power of x. <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>Hence, factored completely, 12 =3D 2*2*3 =3D 22*3.
The Basics<= /span>
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0106.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To factor a number x means to wri= te x as a product, i.e. write x as a*b for some a and b. For example 12 can be factored as
12 =3D 2*6 =3D 3*4 =3D 2*2*3.
We say the factorization is complete if all the factors are = <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>prime numbers. Hence 12=3D2*2<= /span>*3 is factored completely, 2*6 is not complete because 6 is = not a prime number.
Exponents=
To simplify repetitive writing,= we write 22 for 2*2, we write 23 = for 2*2*2, we write 24 for 2*2*2*2 and so on.
Example B:
 
32 =3D 3*3 =3D 9        = ;           (note that 3*2 =3D 6)
43 =3D 4*4*4 =3D 64        = ;       (note that 4*3 =3D 12)
We write x*x*x…*x as xN where N is the number of x’s= multiplied to itself. N is called the exponent, or the power of x. <= span lang=3DEN-US style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;mso-= fareast-font-family: \5B8B\4F53;mso-hansi-font-family:Tahoma;font-size:133%;mso-fareast-languag= e: ZH-CN'>Hence, factored completely, 12 =3D 2*2*3 =3D 22*3.
The Basics<= /span>
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Exponents
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exponents
Basic Laws<= /span>
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0107.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exponents
Basic Laws<= /span>
Associative Law for Addition and Multiplication
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0118.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exponents
Basic Laws<= /span>
Associative Law for Addition and Multiplication
( a + b )  + c =3D a + ( b + c = )
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0119.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
Exponents
Basic Laws<= /span>
Associative Law for Addition and Multiplication
( a + b )  + c =3D a + ( b + c = )        = ;          
( a * b ) * c<= span style=3D'mso-spacerun:yes'>  =3D  a * ( b * c )  
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0120.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exponents
Basic Laws<= /span>
Associative Law for Addition and Multiplication
( a + b )  + c =3D a + ( b + c = )        = ;          
( a * b ) * c<= span style=3D'mso-spacerun:yes'>  =3D  a * ( b * c )        = ;         
Note: We are to perform the operations inside the “(  )”  first. 
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exponents
Basic Laws<= /span>
Associative Law for Addition and Multiplication
( a + b )  + c =3D a + ( b + c = )        = ;          
( a * b ) * c<= span style=3D'mso-spacerun:yes'>  =3D  a * ( b * c )        = ;         
Note: We are to perform the operations inside the “(  )”  first. 
For example,  (1 + 2) + 3 =3D&nbs= p; 3 + = 3 =3D 6,
Exercis= e. 
Factor eac= h of the following numbers completely. Put the = factors fr= om small to large in the exponential notation:  4, 6, = 8, 12, 16,= 18, 24, 27, 32, 36, 45, 48, 56, 60, 63, 72, 75, 81,120
------=_NextPart_01C8EB1E.3D025B50 Content-Location: file:///C:/486BCAB3/1PrimeNumbersandFactors_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Exponents
Basic Laws<= /span>
Associative Law for Addition and Multiplication
( a + b )  + c =3D a + ( b + c = )        = ;          
( a * b ) * c<= span style=3D'mso-spacerun:yes'>  =3D  a * ( b * c )        = ;         
Note: We are to perform the operations inside the “(  )”