find the remainder when 2^2014 is divided by 10

• 2^1 % 10 = 2
  2^2 % 10 => 4%10 = 4
  2^3 % 10 => 8%10 = 8
  2^4 % 10 => 16%10 = 6
  2^5 % 10 => 32%10 = 2
  2^6 % 10 => 64%10 = 4
  .
  .
  The cycle is upto the power of 4... Again it goes on like 2, 4, 8, 6,..
  
  We can write 2014 as --> 4*503+2 [since 4*503=2012... cycle is upto 4th power... so i multiplied with 4...]
  So upto 2012, 503 cycles got over...
  Again next cycle starts with the remainder of 2...
  For the power 2013, remainder=2
  For the power 2014, remainder=4
  
  Ans : 4
  
  
• 10 years agoHelpfull: Yes(24) No(0)
• [REMAINDER = 4]
  Any no. divided by 10 gives the unit digit of that no. as a remainder.
  here,for 2^n expression ,unit digit is repeated every after 4 cycle..
  so, 2^2014 has unit digit = 2014/4=2;unit digit will be 2^2= 4.
  so, remainder will be 4
  
• 10 years agoHelpfull: Yes(1) No(0)
• 2^1 % 10 = 2
  2^2 % 10 => 4%10 = 4
  2^3 % 10 => 8%10 = 8
  2^4 % 10 => 16%10 = 6
  2^5 % 10 => 32%10 = 2
  2^6 % 10 => 64%10 = 4
  2014%4==2
  2^2=4
• 10 years agoHelpfull: Yes(0) No(0)