(((p−1))/p) where p=prime no. Remainder will always be (p−1) or −1 Que. find Remainder ((1!+2!+3!+........................1000!)/(10)) Que. ((1!+2!+3!+........................1000!)/(12)) Que. ((1!+2!+3!+........................1000!)/9) Que. What id the unit digit of below expression 1!+2!+3!+4!+......................1000! ANS. If we divide some number by 100,then remainder is last 2digit similary 1000----Last 3digit 10000 last 4 digit 100000 last 5 digits [(((1+2+3+4+0+0+0+..........+0)/(10))),() ] R=3 unit digit =3


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Question Number 106628 by deep last updated on 06/Aug/20

$\frac{(p - 1)}{p} w h e r e p = p r i m e n o .$ $R e m a i n d e r w i l l a l w a y s b e (p - 1) o r - 1$ $Q u e . f i n d R e m a i n d e r$ $\frac{1! + 2! + 3! + . . . . . . . . . . . . . . . . . . . . . . . . 1000!}{10}$ $Q u e .$ $\frac{1! + 2! + 3! + . . . . . . . . . . . . . . . . . . . . . . . . 1000!}{12}$ $Q u e . \frac{1! + 2! + 3! + . . . . . . . . . . . . . . . . . . . . . . . . 1000!}{9}$ $Q u e . W h a t i d t h e u n i t d i g i t o f b e l o w$ $e x p r e s s i o n$ $1! + 2! + 3! + 4! + . . . . . . . . . . . . . . . . . . . . . . 1000!$ $A N S . I f w e d i v i d e s o m e n u m b e r b y 100, t h e n r e m a i n d e r i s l a s t 2 d i g i t$ $s i m i l a r y 1000 - - - - L a s t 3 d i g i t$ $10000 l a s t 4 d i g i t$ $100000 l a s t 5 d i g i t s$ $[\begin{matrix} \frac{1 + 2 + 3 + 4 + 0 + 0 + 0 + . . . . . . . . . . + 0}{10} \end{matrix}]$ $R = 3$ $u n i t d i g i t = 3$
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