what is the remainder if 100! divided by 97^2?

• as 100!=100*99*98*97..../97*97
  in 100! one 97 is divided by 97*97
  so 1 97 is left for 97*97 it will be only 97
  now 100*99*98*96....(as 97 got cancled) when divided by 97 reminder will be 3
  bcoz their will always last 2 tearm is 00 for 100*99*98*96.....
  consider 100*98=9800 when divided by 97 reminder is 3
  so answer will be 3 when 100! divided by 97^2
• 11 years agoHelpfull: Yes(13) No(17)
• 100*99*98*97*96! mod 97^2 (applied wilson theorm for 96!)
  
  cancel out 97 from numerator and denominator
  
  3*2*1*96 mod 97
  
  576 mod 97
  
  91 mod 97
  
  mos rem is 97*91=8827
• 11 years agoHelpfull: Yes(12) No(2)
• soumik u r wrong ,for xample if u conside 200 which has 00, has a remainder of 2
• 11 years agoHelpfull: Yes(4) No(0)
• vasu pls divide 200 by 97 u will get reminder is 6 and it is multiple of 3. now if u consider the whole 100! thn answer will be 3.
• 11 years agoHelpfull: Yes(0) No(2)
• @jaya i got 1,2 nd and the last line,, but why u calculated 3*2*1 mod 97
• 11 years agoHelpfull: Yes(0) No(0)