factorials

Discussion in 'Undergraduate Math' started by Bill Cunningham, Jan 28, 2011.

  1. I am a little stumped at what this page says. Here's the website.

    http://www.rapidtables.com/math/algebra/Factorial.htm

    In the formula n!=5*(5-1)!=5*24=120

    Where is the 24 coming from? And with strillings apx. as listed on this page
    is the "e" -n Euler's conststant ? Maybe I'm getting this confused with a
    factoring. Is factoring and factorials the same thing?

    Bill
     
    Bill Cunningham, Jan 28, 2011
    #1
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  2. That's (5-1)! = 4!
    "Stirling", not "strilling".
    The symbol "e" is used here for Euler's constant, yes.
    They're related, in that they both have to do with multiplication.

    Factoring is taking a number, such as 21, and determining that it
    can be written as the product of 3 and 7, which are its factors.
     
    Michael Stemper, Jan 28, 2011
    #2
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  3. Ok could I use other numbers here like 5 and 3 if I wanted? It doesn't seem
    to be coming out right.
    If I had a large number like 145 how would I begin beaking it down to
    its mutiplicands? This is probably simple but I need a bit of a refresher.

    Bill
     
    Bill Cunningham, Jan 28, 2011
    #3
  4.  
    Arturo Magidin, Jan 29, 2011
    #4
  5. Arturo Magidin wrote:

    [snip]
    [...]

    I am trying to learn factorials and logarithms right now. I tried for
    example 9! by using 9*8 and it wasn't 45 it was 72 way off. What did I do
    wrong?

    Bill
     
    Bill Cunningham, Jan 29, 2011
    #5
  6. Bill Cunningham

    Stan Brown Guest

    Stan Brown, Jan 29, 2011
    #6
  7. Using the above rule,
    9! = 9 * (9-1)! = 9 * 8!
    Note this is 9 times 8 _factorial_, not 9 times 8.
    As Arturo listed, 8! = 40,320, so 9! = 362,880

    Or you could expand all the way and get
    9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880

    I don't know why you expected 45, that soesn't fit from any of the
    rules
     
    The Qurqirish Dragon, Jan 29, 2011
    #7
  8. I thought the factorial of a number was 1*2*3*4*5*6*7*8*9 for 9!. Am I
    doing this backwards? This series that I am doing reminds me of what is done
    to calculate a weighted average.

    Bill
     
    Bill Cunningham, Jan 29, 2011
    #8
  9. Ok I see now. I guess I was reading the formula wrong.

    Bill
     
    Bill Cunningham, Jan 29, 2011
    #9
  10. 9 factorial is not equal to 9 times 8, it is equal to nine times
    EIGHT FACTORIAL. So you need to figure out what 8! is.

    8! is eight times *seven factorial*.

    Seven factorial is seven times *six factorial*.

    Six factorial is six times *5 factorial*.

    Since we already figured out at 5 factorial is 120, that means that

    6! = 6 * (5!) = 6*(120) = 720.

    Therefore,

    7! = 7*(6!) = 7*(720) = 5040.

    Therefore,

    8! = 8*(7!) = 8*(5040) = 40320.

    So instead of 9 times 8, you should have done 9 times 40320.
     
    Arturo Magidin, Jan 29, 2011
    #10
  11. Multiplication is commutative and associative, so

    9*8*7*6*5*4*3*2*1 is the same as 1*2*3*4*5*6*7*8*9.

    Still doesn't explain why you thought you should get 45. We're
    *multiplying*, not *adding*.
     
    Arturo Magidin, Jan 29, 2011
    #11
  12. Bill Cunningham

    Stan Brown Guest

    It is, but why would you expect it to equal 45? That's what you
    seemed to be saying earlier.
    Well, conventionally factorials are written with the number from high
    to low, but fortunately multiplication is commutative. :)

    Seriously, what do you mean "backwards"?
     
    Stan Brown, Jan 30, 2011
    #12
  13. Arturo Magidin wrote:

    [...]
    Ok yes I should've known this. *brain fart* of course the multiplicative
    property aplies here.

    Bill
     
    Bill Cunningham, Jan 30, 2011
    #13
  14. Ok I misunderstood the formula there.

    Bill
     
    Bill Cunningham, Jan 31, 2011
    #14
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