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

• ans. 1
  sorry for the previous ans
  sol. 5^222 remains which can be written as (7-2)^222
  (-2)^222 remains = 2^222 = 8^74 = (7+1)^74
  thus 1^74 remains which is the remainder
• 11 years agoHelpfull: Yes(29) No(3)
• Using Remainder Theorem,
  (222)^222/7
  ==> 5^222/7
  ==> 4^111/7
  ==> (2^55)*4 /7
  ==> (1)^17*2*2*2*2*4/7
  ==> 64/7
  Remainder is 1
• 11 years agoHelpfull: Yes(17) No(1)
• Answer is 1.
  
• 11 years agoHelpfull: Yes(2) No(2)
• ans. 5
  222 can be written as 217+5
  thus (222)^222 = (217 + 5)^222
  now when the above is divided by 7 all the no in binomial expansion is completely divided except 5^1,as it is not divisible by 7.
  So the remainder is 5.
• 11 years agoHelpfull: Yes(2) No(6)
• 1 is answer.
• 11 years agoHelpfull: Yes(1) No(0)
• (222)^222 can be written as (31*7+5)^222 dividad by 7,den reminder is(5)^222 which is further written as (5^3)^74 =(125)^74 =(18*7-1)^74 which is again divided by 7,den reminder is (-1)^74 is equals to 1,,den we can say finally reminder is 1
• 11 years agoHelpfull: Yes(1) No(0)
• answer = 9
• 11 years agoHelpfull: Yes(0) No(9)
• i want tricks to solve this or same kind of problem.... kindly describe.....
• 11 years agoHelpfull: Yes(0) No(0)
• PINTO DAS if u understand this trick this is the easy way to find out the remainder for this type of problems. I will give u a solution.
  222^222 let written as (2+2+2)^(2+2+2)=6^6=46656. now divide it with 7 i.e 46656/7 gives the remainder as 1
• 11 years agoHelpfull: Yes(0) No(0)