# What is the Notation for Factorials?

• I
• Drakkith
In summary, the notation for factorials is the exclamation mark (!) symbol. To calculate a factorial, you multiply all the numbers from 1 to the given number. Factorial notation is used to represent the number of ways to arrange objects and is commonly used in mathematical equations and probability calculations. Some common examples of factorials include 3!, 4!, and 10!. There is a limit to how large a factorial can be, with the largest factorial that can be calculated with a standard calculator being 69!.
Drakkith
Mentor
I just have a quick question on how to write the notation for a factorial. I have a series with a factorial of 5*10*15*...*(5n) in it. Is this written as 5n!, as (5n)!, or something else? I'm pretty sure it's 5n!, as I've written 5n! out as 5(1*2*3*4*...*n), which when you distribute the 5 appears to come out as (5*10*15*...*5n), but I just wasn't sure if I'd broken some math rule somewhere.

Also, if it is 5n! and not (5n)!, can (5n)! be easily expressed in a form similar to (1*2*3*...*n)?

Thank you!

Drakkith said:
which when you distribute the 5 appears to come out as (5*10*15*...*5n)

Multiplication doesn't distribute over multiplication.

I think you're looking for a quintuple factorial, i.e. ##(5n)!##. For instance, the double factorial is defined as $$(n)!=n \cdot (n-2) \cdot (n-4) ... 1$$

Drakkith
axmls said:
Multiplication doesn't distribute over multiplication.

Hah! Of course it doesn't! Silly me!
@phinds You're rubbing off on me, old man!

axmls said:
I think you're looking for a quintuple factorial, i.e. (5n)!(5n)!(5n)!. For instance, the double factorial is defined as
(n)!=n⋅(n−2)⋅(n−4)...1(n)!=n⋅(n−2)⋅(n−4)...1​
(n)!=n \cdot (n-2) \cdot (n-4) ... 1

Thanks! I'll look into it!

Drakkith said:
I just have a quick question on how to write the notation for a factorial. I have a series with a factorial of 5*10*15*...*(5n) in it
This would be ##5^n(1 * 2 * 3 * ... * n)## or ##5^n * n!##. Each of the n factors in the original expression has a factor of 5, which gives the ##5^n## part, and the remaining part is 1 * 2 * 3 * ... * n, or n!.
Drakkith said:
. Is this written as 5n!, as (5n)!, or something else? I'm pretty sure it's 5n!, as I've written 5n! out as 5(1*2*3*4*...*n), which when you distribute the 5 appears to come out as (5*10*15*...*5n), but I just wasn't sure if I'd broken some math rule somewhere.

Also, if it is 5n! and not (5n)!, can (5n)! be easily expressed in a form similar to (1*2*3*...*n)?

Thank you!

Mark44 said:
This would be 5n(1∗2∗3∗...∗n)5n(1∗2∗3∗...∗n)5^n(1 * 2 * 3 * ... * n) or 5n∗n!5n∗n!5^n * n!. Each of the n factors in the original expression has a factor of 5, which gives the 5n5n5^n part, and the remaining part is 1 * 2 * 3 * ... * n, or n!.

Gah! Somehow I missed the notification that you replied last night, Mark. I was just about to post the correct notation, which is 5nn!. Just got help from a tutor here on campus who figured it out. It all makes perfect sense now!

All these exclamation marks . . . everyone is so excited!

## What is the notation for factorials?

The notation for factorials is the exclamation mark (!) symbol. For example, 5 factorial is written as 5!.

## How do I calculate factorials?

To calculate a factorial, you multiply all the numbers from 1 to the given number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

## What is the purpose of using factorial notation?

Factorial notation is used to represent the number of ways to arrange a certain number of objects in a specific order. It is also used in mathematical equations and probability calculations.

## What are some common examples of factorials?

Some common examples of factorials include 3! = 3 x 2 x 1 = 6, 4! = 4 x 3 x 2 x 1 = 24, and 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800.

## Is there a limit to how large a factorial can be?

Yes, there is a limit to how large a factorial can be. The largest factorial that can be calculated with a standard calculator is 69!. After that, the result is too large to be displayed. However, using advanced mathematical techniques, larger factorials can be calculated.

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