what will be the remainder when (222)^222 is divided by 7??

• (222^222)/7 by remainder theorem, we get remainder of 222/7 is 5.. 5^222;
  5^2*111; 25^111; remind(25/7)=4; 4^111;
  4^(3*37);
  (4*4*4)^37;
  64^37; remind(64/7)=1;
  1^37=1
  so the remainder is 1
• 11 years agoHelpfull: Yes(45) No(3)
• it
  is 1
  as 222^222>>>>5^222>>>>>>4^111=64^37>>>>>>1^37=1
• 11 years agoHelpfull: Yes(7) No(4)
• i think the remainder is 4
• 11 years agoHelpfull: Yes(6) No(3)
• Answer is 01
  Using Remainder Theorem
  222^222 reduces to 5^222
  now,
  it reduces to 4^111
  again 4 * (2)^55
  again 4* (1)^18 * 2
  which is equal to 8/7
  which gives the remainder as 01
• 11 years agoHelpfull: Yes(4) No(3)
• the remainder is 4
  222^222/7=(5^222)/7
  =(25^111)/7
  =(4^111)/7
  =(8^55*4)/7
  =(1^55*4)/7
  =4/7. Hence remainder is 4
• 11 years agoHelpfull: Yes(2) No(1)
• answer is 4..[because the unit digit must be divisible by 10.so,the value is 2^222...2^222 can be write like this..2^4*55+2=2^2=4(2^1=2,2^2=4,2^3=8,2^4=6,2^5=2^4*2=2..the cycle can be repeated).so,the dividend is 4..the ans is 4/7=4]
• 11 years agoHelpfull: Yes(1) No(0)
• pls someone explain the remainder theorem...
• 11 years agoHelpfull: Yes(1) No(0)
• 222^222/7->when base 222/7 it gives +5 as +ve integer and -2 as -ve integer
  in order to simplify the solution i prefer -2 so(-2)^222/7
  again 2^222 can be written as (-2^3)^37*2^2 (nothing but -2^222)
  then (-2^3)=-8 which gives -1 as -ve integer so(+1)^37 nothing but 1 there again 2^2 was remained which gives us 4 as the answer
• 11 years agoHelpfull: Yes(1) No(0)
• from remainder theorem
  222/7=remainder(5)
  5^222=(25^111)
  25/7=remainder4
  4^111=4*4^110
  4*2^55
  4*1^18*2
  8/7=1
• 11 years agoHelpfull: Yes(0) No(2)
• remainder is 3
  
• 11 years agoHelpfull: Yes(0) No(2)
• 1 is the remainder :)
• 11 years agoHelpfull: Yes(0) No(0)