Factorial/Examples

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Examples of Factorials

The factorials of the first few positive integers are as follows:

$\begin{array}{r|r} n & n! \\ \hline 0 & 1 \\ 1 & 1 \\ 2 & 2 \\ 3 & 6 \\ 4 & 24 \\ 5 & 120 \\ 6 & 720 \\ 7 & 5 \, 040 \\ 8 & 40 \, 320 \\ 9 & 362 \, 880 \\ 10 & 3 \, 628 \, 800 \\ \end{array}$

This sequence is A000142 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Factorial of $0$

The factorial of $0$ is $1$:

$0! = 1$


Factorial of $1$

The factorial of $1$ is $1$:

$1! = 1$


Factorial of $10$

$10! = 3 \, 628 \, 000$


Factorial of $11$

$11! = 39 \, 916 \, 800$


Factorial of $12$

$12! = 479 \, 001 \, 600$


Factorial of $13$

$13! = 6 \, 227 \, 020 \, 800$


Factorial of $14$

$14! = 87 \, 178 \, 291 \, 200$


Factorial of $15$

$15! = 1 \, 307 \, 674 \, 368 \, 000$


Factorial of $16$

$16! = 20 \, 922 \, 789 \, 888 \, 000$


Factorial of $17$

$17! = 355 \, 687 \, 428 \, 096 \, 000$


Factorial of $18$

$18! = 6 \, 402 \, 373 \, 705 \, 728 \, 000$


Factorial of $19$

$19! = 121 \, 645 \, 100 \, 408 \, 832 \, 000$


Factorial of $20$

$20! = 2 \, 432 \, 902 \, 008 \, 176 \, 640 \, 000$


Factorial of $21$

$21! = 51 \, 090 \, 942 \, 171 \, 709 \, 440 \, 000$


Factorial of $22$

$22! = 1 \, 124 \, 000 \, 727 \, 777 \, 607 \, 680 \, 000$


Factorial of $23$

$23! = 25 \, 852 \, 016 \, 738 \, 884 \, 976 \, 640 \, 000$


Factorial of $24$

$24! = 620 \, 448 \, 401 \, 733 \, 239 \, 439 \, 360 \, 000$


Factorial of $25$

$25! = 15 \, 511 \, 210 \, 043 \, 330 \, 985 \, 984 \, 000 \, 000$


Prime Factors of $39!$

The prime decomposition of $39!$ is given as:

$39! = 2^{35} \times 3^{18} \times 5^8 \times 7^5 \times 11^3 \times 13^3 \times 17^2 \times 19^2 \times 23 \times 29 \times 31 \times 37$


Factorial of $52$

The number of ways there are to shuffle a $52$-card deck is given by:

$52! = 806 \ 58175 \ 17094 \ 38785 \ 71660 \ 63685 \ 64037 \ 66975 \ 28950 \ 54408 \ 83277 \ 82400 \ 00000 \ 00000$


Prime Factors of $52!$

The prime decomposition of $52!$ is given as:

$52! = 2^{49} \times 3^{23} \times 5^{12} \times 7^8 \times 11^4 \times 13^4 \times 17^3 \times 19^2 \times 23^2 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47$


Factorial of $450$

\(\displaystyle 450!\) \(=\) \(\displaystyle 17333 \, 68733 \, 11263 \, 26593 \, 44713 \, 14610 \, 45793 \, 99677 \, 81126 \, 52090\)
\(\displaystyle \) \(\) \(\displaystyle 51015 \, 56920 \, 75095 \, 55333 \, 00168 \, 34367 \, 50604 \, 67508 \, 82904 \, 38710\)
\(\displaystyle \) \(\) \(\displaystyle 61458 \, 11284 \, 51842 \, 40978 \, 58618 \, 58380 \, 63016 \, 50208 \, 34729 \, 61813\)
\(\displaystyle \) \(\) \(\displaystyle 51667 \, 57017 \, 19187 \, 00422 \, 28096 \, 22372 \, 72230 \, 66352 \, 80840 \, 38062\)
\(\displaystyle \) \(\) \(\displaystyle 31236 \, 93426 \, 74135 \, 03661 \, 01015 \, 08838 \, 22049 \, 49709 \, 29739 \, 01163\)
\(\displaystyle \) \(\) \(\displaystyle 67937 \, 66165 \, 02373 \, 08538 \, 96403 \, 90159 \, 08361 \, 44149 \, 59443 \, 26842\)
\(\displaystyle \) \(\) \(\displaystyle 04513 \, 78471 \, 64023 \, 03182 \, 60409 \, 46839 \, 93315 \, 06130 \, 25639 \, 18385\)
\(\displaystyle \) \(\) \(\displaystyle 30334 \, 15106 \, 06761 \, 46242 \, 02058 \, 20006 \, 93635 \, 20959 \, 67417 \, 18319\)
\(\displaystyle \) \(\) \(\displaystyle 15387 \, 25617 \, 50952 \, 13805 \, 56781 \, 30919 \, 54298 \, 00229 \, 27380 \, 33425\)
\(\displaystyle \) \(\) \(\displaystyle 53558 \, 16459 \, 19962 \, 98912 \, 36859 \, 85477 \, 71179 \, 15846 \, 13513 \, 40068\)
\(\displaystyle \) \(\) \(\displaystyle 90564 \, 71276 \, 58164 \, 83637 \, 71263 \, 03774 \, 92336 \, 00780 \, 72307 \, 46200\)
\(\displaystyle \) \(\) \(\displaystyle 85543 \, 55068 \, 36144 \, 81266 \, 06281 \, 14576 \, 09604 \, 99187 \, 81342 \, 83979\)
\(\displaystyle \) \(\) \(\displaystyle 24840 \, 59250 \, 45378 \, 49487 \, 42506 \, 04884 \, 81036 \, 57144 \, 79570 \, 46788\)
\(\displaystyle \) \(\) \(\displaystyle 63574 \, 29367 \, 14615 \, 17621 \, 91484 \, 69743 \, 10297 \, 99497 \, 40714 \, 48510\)
\(\displaystyle \) \(\) \(\displaystyle 47161 \, 69664 \, 05239 \, 73926 \, 02848 \, 40869 \, 40074 \, 08998 \, 90112 \, 74929\)
\(\displaystyle \) \(\) \(\displaystyle 05171 \, 51447 \, 34313 \, 86633 \, 39249 \, 20406 \, 61522 \, 69230 \, 30438 \, 13960\)
\(\displaystyle \) \(\) \(\displaystyle 54196 \, 60932 \, 24243 \, 80922 \, 51372 \, 68851 \, 71790 \, 43032 \, 14058 \, 23844\)
\(\displaystyle \) \(\) \(\displaystyle 79361 \, 11678 \, 56823 \, 69730 \, 36238 \, 40462 \, 65078 \, 90688 \, 00000 \, 00000\)
\(\displaystyle \) \(\) \(\displaystyle 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000\)
\(\displaystyle \) \(\) \(\displaystyle 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 00000 \, 0\)


Factorial of $1\,000$

The factorial of $1\,000$ starts:

$402,387,260,077 \ldots$

and has $2568$ digits, of which the last $249$ are $0$.


Factorial of $1\,000\,000$

The factorial of $1 \, 000 \, 000$ has $5 \, 569 \, 709$ digits.


Sources