# factorials

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

1. ### Bill CunninghamGuest

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

2. ### Michael StemperGuest

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

3. ### Bill CunninghamGuest

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
4. ### Arturo MagidinGuest

Arturo Magidin, Jan 29, 2011
5. ### Bill CunninghamGuest

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
6. ### Stan BrownGuest

Stan Brown, Jan 29, 2011
7. ### The Qurqirish DragonGuest

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
8. ### Bill CunninghamGuest

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
9. ### Bill CunninghamGuest

Ok I see now. I guess I was reading the formula wrong.

Bill

Bill Cunningham, Jan 29, 2011
10. ### Arturo MagidinGuest

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
11. ### Arturo MagidinGuest

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

Arturo Magidin, Jan 29, 2011
12. ### Stan BrownGuest

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
13. ### Bill CunninghamGuest

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
14. ### Bill CunninghamGuest

Ok I misunderstood the formula there.

Bill

Bill Cunningham, Jan 31, 2011