A factorial is the result of multiplying all of the whole numbers in a given number. So, for the number 405, you would multiply it as follows:
Therefore, the answer to the question "what is the factorial of 405?" is:
As you can probably imagine, the size of a factorial for a given number grows exponentially as the number increases and it takes more and more computing power in order to calculate it. In the next section, we'll discuss why you might want to know what the factorial of 405 is and why it's useful in mathematics.
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Factorials are usually written with the given number followed by an exclamation mark after it:
What are Factorials Used For?
On the surface, you might wonder why factorials are even important and why we would want to use them. Factorials are a useful method for a number of different mathematical problems, particularly those involving probability or calculus with a series.
So for example, let's say you have 405 books on a bookshelf. You want to work out how many different ways those books can be arranged on the shelf.
You could do this via trial and error, putting the books into a different order on the shelf, recording the order, and then rearranging. This would be repeated until there are no other possibilities.
Obviously that would take a lot of time, particularly if you're dealing with a library full of books. The easier way would be to use factorials, and by performing the calculation above, we can see exactly how many different combinations that could be taken.
There are many more complicated uses of factorials than this such as calculating binomials, astronomy, or advanced calculus but hopefully this helps you to understand it purely from a "how many different ways can the given items be arranged".
When writing out a factorial as 405!, there are a couple of different ways to say it:
- 405 factorial
- 405 shriek
- 405 bang
Our personal favorite is 405 shriek 🙀.
Give this a try for yourself and try to calculate some factorials for yourself using a pen and paper. Just make sure not to pick a number that is too large or you will need a lot of paper to write down the answer!
You can also use the factorial calculator below to find the factorial of numbers up to 500.
Calculate Another Factorial
Enter your number in box A below and click "Calculate" to work out the factorial of the number.