what is the remainder when 1212121212....(upto 300 digits) is divided by 99 ?

• Taking 1st 4 digits
  1212/99 and the remainder is 24
  
  now 12121212/99 = remainder 48 = 2*24
  
  so for 300/4 digits = remainder = 75*24 =1800/99=18
  
  so 18 is the correct answer... :-)
• 11 years agoHelpfull: Yes(28) No(3)
• ans=18
  1212121212.........upto300 /99
  (12)(12)(12).........upto150
  if 12 is divided by 99 then remainder is 12
  therefor 150*12=1800/99=rem=18
  :-)
• 11 years agoHelpfull: Yes(17) No(1)
• 121212.....
  => 12(101010101010........300 times)/99
  => 12(10^298 + 10^296 + 10^294+..........+ 10^0)/99
  =>12((10^2)^149+(10^2)^148+(10^2)^147+..........+(10^2)^0))/99
  =>12(1+1+1+.....150 times)/99 (as 100mod99=1)
  =>12*150/99
  =>1800/99
  ans is 18
• 11 years agoHelpfull: Yes(6) No(0)
• here 12 is used again and again......so
  12%99=12(remainder)
  1212%99=24(remainder)=12*2
  121212%99=36(remainder)=12*3
  we get that...remainders are multiplication of 12
  so,here 12 used 150 times.....
  therefor 150*12=1800
  remainder=1800/99=18
  ans is 18
• 11 years agoHelpfull: Yes(4) No(0)
• for 1212/99 remainder is 24*1
  for 12121212/99 remainder is 24*2
  for 121212121212/99 remainder is 24*3
  
  for 12121212121212....300 digits 24*75 =1800/99 = 18 (ans)
• 11 years agoHelpfull: Yes(1) No(0)
• answer is correct by @nimish goel
  
• 11 years agoHelpfull: Yes(1) No(0)
• divide 12 by 99 the remainder is 12..
  now by making 300 into two parts that is 150..now 12*150=1800
  divide 1800 by 99 the remainder is 18
• 10 years agoHelpfull: Yes(0) No(0)