222^222 divided by 7 … what is the reminder ?

• perhaps 1 is the answer
• 12 years agoHelpfull: Yes(12) No(1)
• 222^222
  =(2*111)^222
  =2^222*111^222
  =(8)^74*(111)^222
  =8 divided by 7 gives remainder 1...so 8^74/7=1
  =(111)/7 gives remainder 6..so
  =(6)^222/7
  =36^111/7
  =36*36*36...222 gives remainder 1
  so 1*1=1
  1 is the remainder
  
  
• 12 years agoHelpfull: Yes(11) No(1)
• unit digit of 222^222=4
  222^1=2
  222^2=4
  222^3=8
  222^4=6
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  222^12=6
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  222^22=4
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  222^32=6
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  222^42=4
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  222^222=4
  so the reminder(4)/7=4
  answer is=4
• 12 years agoHelpfull: Yes(5) No(11)
• 222/7 the reminder is 5 or -2 so by reminder theorem it becomes (-2)^222...so 2 powers has 3 cycle when it is divided by 7 like 2,4,1..as 2^1 is divided by 7 we get 2 like that ..222 is perfectly divided by 3 so it is 3rd term of 2,4,1 cycle that is 1..
  
• 12 years agoHelpfull: Yes(2) No(2)
• goldy can u pls explain it by elaborating
• 12 years agoHelpfull: Yes(1) No(2)
• as above 222^2=49284
• 12 years agoHelpfull: Yes(0) No(2)
• we take un it digit &power of this div by 4 remainder comes becomes power of u's digit 2^2=2(mod7)=4
• 12 years agoHelpfull: Yes(0) No(3)