The factorial is a very important measure in combinatorics. It indicates how many ways there are to arrange different things. The factorial is defined for natural numbers, i.e., 1, 2, 3, and so on. The calculation is very simple: the factorial of a natural number is the product of this number and all other smaller natural numbers. It is written as a number with an exclamation mark after it. n! = 1 * 2 * 3 * ... * n-1 * n
Of course, there is only one way to arrange one thing; with two things, there are two possibilities. Starting with three things, the number of possibilities increases significantly, now there are six. If you want to arrange five different things next to each other in a row, you have 5!, which is 120 possibilities. So the factorial grows very rapidly and quickly leads to very large values. 20! is already 2432902008176640000, a two with 18 following digits, which is two quintillion.
Enter a natural number and click Calculate to calculate the factorial. The output is in standard decimal notation. However, since the values can be very large, the result is also given in exponential notation.
For values greater than four, all factorials end in at least one zero. The reason for this is that starting with five, there is a 2 and a 5, so the calculation always contains a multiplication by 10. For even larger factorials, 10, 20, and so on are included as multipliers, and so on, so that the number of ending zeros continues to increase.
In addition to this mathematically simple form for calculating various arrangements, the factorial appears in many, sometimes quite complicated, formulas in combinatorics and probability theory. A somewhat more complicated calculation, which also appears relatively frequently and contains factorials, is the binomial coefficient.
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