what is the remainder when 100! is divided by 97^2?
1.582 2.8148 3.1261 4.8827

• first understand dis
  (6*10*55)/9
  remainder of this is 6. there r two ways to calculate this
  1--- 6*10*55 ie 3300 mod 9 = 6
  2--- 6 mod 9 =6
  10 mod 9 =1
  55 mod 9=1
  thn multiply all the rem n u get the ans ie 6
  
  in case of 97^2
  100*99*98*97*96! / 97^2
  97 will b cancel out
  100*99*98*96 ! / 97
  nw find out remainder individually
  100 % 97 =3
  99 % 97 =2
  98 % 97=1
  and acc to wilson theorem
  if p is a prime no thn (p-1)! mod p =-1
  here 97 is a prime no so
  96!% 97 = -1 or 96
  so multiply all the rem
  3 * 2*1* 96 mod 97 = 576 mod 97 = 91
  nw multiply 91 with 97 so we get
  91*97= 8827
• 12 years agoHelpfull: Yes(28) No(4)
• Wilson Theorem ???
  How does dat come by ??
  and how to apply it ??
  Wilson Theorem is for Prime No. and 96 is NOT a prime ...
  Please elaborate a bit more !!!
  Thx !!
• 12 years agoHelpfull: Yes(10) No(0)
• 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
• 12 years agoHelpfull: Yes(8) No(9)
• 8827 is the remainder when 100! is divided by 97^2.
• 12 years agoHelpfull: Yes(4) No(1)
• @kajal sharma
  plzz xplain, why u multiplied by 97 in last line? i.e 91*97 :/
• 11 years agoHelpfull: Yes(3) No(0)
• Please give the Explanation !!!!
• 12 years agoHelpfull: Yes(2) No(1)
• 97 is a prime number.
• 12 years agoHelpfull: Yes(2) No(1)
• @smita pls help us to understand the solution
  explain why u did this
  3*2*1*96 mod 97
• 12 years agoHelpfull: Yes(0) No(2)