Remainder when 1212121212....... (up to 300 digits) is divided by 99?

• 12 / 99 => rem = 12*1
  
  1212 / 99 => rem = 12*2
  
  121212 / 99 => rem = 12*3
  
  12121212 / 99 => rem = 12*4
  
  same way
  
  1212121212....... (up to 300 digits) / 99 => 12*150 / 99 => 18
• 9 years agoHelpfull: Yes(21) No(3)
• Rahul, just check the remainder when we take 12 /99 that is 12 is two digit rem 12*1 then 1212 it is four digit , that is 12*2 so 12......(300dgt) then 12*150 hope you got it
  
• 9 years agoHelpfull: Yes(4) No(0)
• RAKESH i dont understand why do you divide 12*150 by 99.we are already getting remainder 12*150 by dividing numbers with 99..so why do you again divide 12*150 by 99 in the last line????????? plz clarify ....it.........
• 9 years agoHelpfull: Yes(3) No(0)
• 121212121212.......(upto 300 digits) when divided by 3 gives
  404040404040........(upto 299 digits), this when divided by 3 gives
  134680134680134680..........13468,
  then sum of odd place digits = 50*(1+4+8)=50*13
  sum of even place digits =50*(3+6)=50*9
  odd-even=50*4=200
  200/11 we get remainder 2
  therefore ans=2
• 9 years agoHelpfull: Yes(2) No(3)
• 12/99 rem=12
  1212/99 rem=24=12*2
  121212/99 rem=36=12*3
  (12)(12).....150 tims/99 rem=12*150
  (12*150)/99 rem=18
• 9 years agoHelpfull: Yes(2) No(0)
• rahul, we again divide because 12*150 is greater than 99.
• 9 years agoHelpfull: Yes(1) No(0)
• (12*150)/99 rem is 8
• 9 years agoHelpfull: Yes(1) No(2)
• 12(10^298+10^296+....10^2+1)%99
  12(100^149+100^148....100+1)%99
  12(1+1+1.............+1 150terms)%99
  12(150)%99
  (12*51)%99
  612%99
  18 ans
  
• 9 years agoHelpfull: Yes(1) No(1)