
faaktariyon

samkhyaa sidhaanthathil, oru nischitha samkhyayude adisthaana soothravaakyathile oru faaktariyon athinte akkangalude faaktariyalukalude koottatthinu thulyamaaya oru swaabhaavika samkhyayaanu. clifford eiii enna ezhuthukaaranaanu faaktariyon enna peru srishtichathu. pickover.
nirvachanam.
soothravaakyam _ 2 oru swaabhaavika samkhyayaayirikkatte. oru adisthaana soothravaakyam _ 3-nuu, formula _ 2, formula _ 5-nte akkangalude faaktoriyalukalude aakethuka inipparayunna reethiyil nirvachikkunnu
adisthaana soothravaakyam _ 1 leeii samkhyayile akkangalude ennamaanu formula _ 7, formula _ 9 formula _ 2 nte faaktoriyalaanu, 
samkhyayude 12-aamm akka soothravaakyathinte moolyamaanithu. oru swaabhaavika samkhyayude soothravaakyam _ 2 ennathu soothravaakyam _ 15, i-yude oru nischitha binduvaanenkil oru soothravaakyam _ 1 faaktariyon aanu.iii. formula _ 16. formula _ 17 umm formula _ 18 umm ellah bays formula _ 1-num nischitha pooyintukalaanenkil, athinaal ellah formula _ 1-num nissaramaaya faaktariyanukalaanenkil, matellaa faaktariyanukalum nissaaramallaattha faaktariyanukalaanu. 
udaaharanathinu, adisthaana soothravaakyamaaya _ 21 leeii 145 enna samkhya oru faaktariyon aanu, kaaranam soothravaakyam _ 22 aanu. 
formula _ 23-neey sambandhichidatholam, akkangalude faaktoriyalukalude aakethuka formula _ 25 muthal bays 2 praathinidhyatthile formula _ 24 enna akkangalude ennamaanu. 
oru positteev poornnasankhya formula _ 24-nuu formula _ 28 roopappedukayum, 24-aamm kaalayalavile formulayude oru chakram roopappedukayum cheiyunna formula _ 15-nte periodic poyintaanengil, oru swaabhaavika samkhya formula _ 2 oru soshable faaktariyon aanu. oru faaktariyon formula _ 31 ulla oru soshable faaktariyon aanu, koodaathe oru amicable faaktariyon formula _ 32 ulla oru soshable faaktariyon aanu.
adisthaana samkhya enthuthanneyaayaalum ellah swaabhaavika samkhyakalude soothravaakyavum soothravaakyavum 15-nte preperodic poyintukalaanu. kaaranam, 24 akkangalude soothravaakyamulla adisthaana soothravaakyathinte ellah swaabhaavika samkhyakalum soothravaakyam 37-neey thripthippeduthunnu. ennirunnaalum, soothravaakyam 38 aayirikkumbol, soothravaakyam 40-nuu formula 39, athinaal eathu soothravaakyam _ 2 formula 43 vare soothravaakyam _ 42-neey thripthippeduthum. formula _ 44-nekkaal parimithamaaya niravadhi swaabhaavika samkhyakalundu, athinaal samkhya oru periodic poyintiloo formula _ 45-nekkaal kuranja oru nischitha poyintiloo athumennu urappaan, ithu oru preperiodic pooyintaayi maarunnu. formula _ 23-nuu, eathu samkhyayudeyum akkangalude samkhya formula _ 47, orikkal koodi, athine oru preperodic pooyintaayi maattunnu. ithinartham eathenkilum adisthaana soothravaakyam _ 1 nuu parimithamaaya ennam faaktoriyanukalum saikkilukalum undennum. 
oru nischitha binduviletthaan formula _ 50 nuu aavashyamaaya aavarthana formula _ 12 nte ennam formula _ 15 functionte formula _ 2 nte sthirathayaanu, athu orikkalum oru nischitha binduvil athunnillengil nirvachikkappettitla.
faaktarikal.
"b" = ("k" −1)!
formula _ 24 oru positteev poornnasamkhyayum samkhyayude adisthaana formula _ 54 umm ayirikkatte.
"bii" = "keey"! - "k" + 1.
formula _ 24 oru positteev poornnasamkhyayum nambar bays formula _ 62 umm aakatte.
faaktoriyanukaludeyum cycleukaludeyum pattika.
ellah samkhyakalum adisthaana soothravaakyathil prathinidheekarikkunnu.