▁in ▁Lag hou at ▁Province ▁Category : Comm unes ▁of ▁Al ger ia <0x0A> </s> ▁Tri al ▁division ▁is ▁the ▁most ▁labor ious ▁but ▁easiest ▁to ▁understand ▁of ▁the ▁integer ▁factor ization ▁algorithms . ▁ ▁The ▁essential ▁idea ▁behind ▁trial ▁division ▁tests ▁to ▁see ▁if ▁an ▁integer ▁n , ▁the ▁integer ▁to ▁be ▁fact ored , ▁can ▁be ▁divided ▁by ▁each ▁number ▁in ▁turn ▁that ▁is ▁less ▁than ▁n . ▁ ▁For ▁example , ▁for ▁the ▁integer ▁, ▁the ▁only ▁numbers ▁that ▁divide ▁it ▁are ▁ 1 , ▁ 2 , ▁ 3 , ▁ 4 , ▁ 6 , ▁ 1 2 . ▁ ▁Select ing ▁only ▁the ▁largest ▁powers ▁of ▁pr imes ▁in ▁this ▁list ▁gives ▁that ▁. ▁ ▁Tri al ▁division ▁was ▁first ▁described ▁by ▁F ib on acci ▁in ▁his ▁book ▁Liber ▁Ab aci ▁( 1 2 0 2 ). ▁ ▁Method ▁ ▁Given ▁an ▁integer ▁n ▁( n ▁refers ▁to ▁" the ▁integer ▁to ▁be ▁fact ored "), ▁the ▁trial ▁division ▁consists ▁of ▁system atically ▁testing ▁whether ▁n ▁is ▁divis ible ▁by ▁any ▁smaller ▁number . ▁Clear ly , ▁it ▁is ▁only ▁worth while ▁to ▁test ▁candidate ▁factors ▁less ▁than ▁n , ▁and ▁in ▁order ▁from ▁two ▁up wards ▁because ▁an ▁arbitrary ▁n ▁is ▁more ▁likely ▁to ▁be ▁divis ible ▁by ▁two ▁than ▁by ▁three , ▁and ▁so ▁on . ▁With ▁this ▁ordering , ▁there ▁is ▁no ▁point ▁in ▁testing ▁for ▁divis ibility ▁by ▁four ▁if ▁the ▁number ▁has ▁already ▁been ▁determined ▁not ▁divis ible ▁by ▁two ,