2007-03-27 20:30:47 · 6 answers · asked by Abhijit H 1 in Science & Mathematics ➔ Mathematics
Stirling's formula gives a reasonable
approximation to n! for n > 10.
n! ≈ n^n * e^(-n) * sqrt(2 * pi * n)
285714! ≈ 285714^285714 * e^(-285714) * sqrt(2 * pi * 285714)
Convert each term to 10^power, then add powers.
≈ 10^1558836.0186924297025253327312103 * 10^-124084.01360250569268551464793934 * 10^3.1270556948565701817144928031148
≈ 10^1434755.1321456188664099997977635
≈ 1.35564 * 10^(1434755)
(All done using Windows calculator, but after
checking Mathematica's result, this one seems
to be accurate to only 6 figures - I have no
knowledge as to how accurate the method is.)
EDIT: There seem to be some dots added as the
numbers were too long, but if you put the cursor
over the numbers, they will become visible.
2007-03-28 02:13:26 · answer #1 · answered by falzoon 7 · 0⤊ 0⤋
This number identifies if a number is a factorial.
It appears the number 285714 is not a factorial result.
Take the number under test, and keep dividing it down by the natural numbers until you get one.
N / 1 = N
N / 2 = N2
N2 / 3 = N3
N4 / 4 = N5
N5 / 5 = N6 ......and so on.
Take for example the number 720.
720 / 1 = 720
720 / 2 = 360
360 / 3 = 120
120 / 4 = 30
30 / 5 = 6
6 / 6 = 1
The highest number you divided by was 6 (natural number), so factorial 6 = 720.
6 ! = 720.
2007-03-27 20:51:24 · answer #2 · answered by Brenmore 5 · 0⤊ 0⤋
Use excel. The formula is =fact(285714)
wait - never mind. that number blows up excel. LOL!
2007-03-27 20:39:18 · answer #3 · answered by Anonymous · 0⤊ 1⤋
Mathematica 5.1 does it quickly. But the answer is too big to fit here. But it starts
13556442787163913627316670135095917407355402300549000005188919615398114292496....then it goes on and on...
It has 1,434,756 digits in the number, and it ends in 0 [of course ;)]
2007-03-27 20:50:07 · answer #4 · answered by William E 2 · 0⤊ 0⤋
Use mathematica or matlab or any mathematical software.
2007-03-27 20:56:15 · answer #5 · answered by Anonymous · 0⤊ 0⤋
use mathematica...
285714!=135564427871639136273166701350959174073554023005490000051889196153981142924968\
344123595085866481501662949153370928161154075768126807690341869988261147840781\
510856510039304935614683409103707431327752362917088449624326544451898812442008\
673637516558583085570644829681727135793977936123345252211676749605104214635931\
589432395641420885793222975519808870613873143294823630333105169672307073161653\
602999087437177733765630024344899237944447538018812200391761512207842843521517\
806067368324306086605282963612066765687939223600392048048085421785538311690668\
459415427877777068393392198467104292885730504669470334363190952007350163535312\
165889454275919794381818791832193284899066019593821113090118794190748285654165\
133996285022898929268214037913398208298086866735700622473052945761298240582515\
801388062399899368815487720536900763929255854074584069730969815632276645861892\
105367081172961575066733507954689436653110790158334365058477645576475198139743\
693156538377017956644672295131929948839265035508791884924871720074296577713090\
297594942795519420674678376690838166153599183090808401730231075246021727480135\
480760384693684236229228043062510222989933715852696645803231547558404906514181\
126712631476383123987843583131874824906438670820894821224407917537777172767908\
407996416868919953678589407062916667649220273172101602316188578901974656795896\
902706121305433979654050547164421411287895767540767723564920632588860306906182\
424074891944476730544768242919042781517595477398126505706598405567903397510678\
728870828625048922723935374398635864162871245455130731421776320841498360349271\
59373604569015085370693010725355909548526335 and 10 times goes on like this
2007-03-27 20:43:33 · answer #6 · answered by Birim 3 · 1⤊ 0⤋