find the remainder when 3^164 divided by 162

• remainder is 1...
  
  we can write 162 as 2*81=2*(3^4)
  so (3^164)/(2*(3^4))=(3^160)/2
  3 power any thing will result an odd integer... ( like 3,9,27,81...)
  so 3^160 is an odd integer...
  we all know any odd integer divided by 2 will result 1 as remainder...
  so 1 is the remainder...
• 11 years agoHelpfull: Yes(18) No(4)
• 3^1=3
  3^2=9
  3^3=27 units place 7
  3^4=81 units place 1
  ---------------------
  3^5=243 units place 3
  3^6=--9 units place 9
  '
  '
  '
  3^160=----1 units place 1
  
  3^164/162=3^164/2*3^4
  =3^160/2
  =(---1)/2=rem(1)
  so, remainder=1
• 11 years agoHelpfull: Yes(3) No(4)
• For x ≥ 4, Remainder (
  3x
  81
  )=0
  And, Remainder (
  3x
  162
  )= 81
• 10 years agoHelpfull: Yes(1) No(1)
• ans is 81
  
• 7 years agoHelpfull: Yes(1) No(0)
• Answer is 2.
  
  1+6+4=11. Nearest multiple of 3 is 9. So the difference is remainder = 2.
• 11 years agoHelpfull: Yes(0) No(16)