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The n-compositorial is equal to the n-factorial divided by the primorial n#. The compositorials are 1, 4, 24, 192, 1728, 17 280, 207 360, 2 903 040, 43 545 600, 696 ...
4.023 872 601 × 10 2 567: 3 249: ... In mathematics, the factorial of a non-negative integer ... Divide all of the exponents by two (rounding down to an integer ...
= ((((3×5 + 4)×4 + 1)×3 + 0)×2 + 1)×1 + 0 = 463 10. (The place value is the factorial of one less than the radix position, which is why the equation begins with 5! for a 6-digit factoradic number.) General properties of mixed radix number systems also apply to the factorial number system.
For each of the values of n from 2 to 30, the following table shows the number (n − 1)! and the remainder when (n − 1)! is divided by n. (In the notation of modular arithmetic, the remainder when m is divided by n is written m mod n.) The background color is blue for prime values of n, gold for composite values.
2520 is: . the smallest number divisible by all integers from one to ten, i.e., it is their least common multiple.; half of 7! (), meaning 7 factorial, or the product of five consecutive numbers, namely .
Since ! is the product of the integers 1 through n, we obtain at least one factor of p in ! for each multiple of p in {,, …,}, of which there are ⌊ ⌋.Each multiple of contributes an additional factor of p, each multiple of contributes yet another factor of p, etc. Adding up the number of these factors gives the infinite sum for (!
To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [5] It is a ratio in the order of about 10 80 to 10 90 , or at most one ten-billionth of a googol (0.00000001% of a googol).
In number theory, the Kempner function [1] is defined for a given positive integer to be the smallest number such that divides the factorial!. For example, the number 8 {\displaystyle 8} does not divide 1 ! {\displaystyle 1!} , 2 ! {\displaystyle 2!} , or 3 ! {\displaystyle 3!} , but does divide 4 ! {\displaystyle 4!} , so S ( 8 ) = 4 ...