222 ^ 222, divided by 7, what is the remainder ?

• 222^6 = 1 mod 7
  222^222 = (222^6)^37 = 1^37 mod 7 = 1 mod 7
  ==> remainder = 1
  
• 9 years agoHelpfull: Yes(10) No(0)
• 222^222/7=5^222/7(because after dividing 222 by 7 we get 5 as remainder)
  ((5^3)^74)/7=125^74/7=(126-1)^74/7=(7*9-1)74/7=1 as remainder (74 is even)
• 9 years agoHelpfull: Yes(1) No(0)
• take tens and units place of 222, i.e 22
  22/7 remainder is 1.
  therefore there r 222 ones
  i.e 1^222
  (1^222)/7 =1/7
  the remainder is 1.
• 7 years agoHelpfull: Yes(1) No(0)
• remainder = 1 . As 222 mod 6=0 .
• 9 years agoHelpfull: Yes(0) No(1)
• We can use fermat little theorem to solve this question.
  222^222/7=5^222/7
  Fermat's little theorem = a^p−1/p=1
  Here P should be prime
  So 5^222/7=(5^6)^37/7=1^37/7=1
  So the remainder is 1.
• 8 years agoHelpfull: Yes(0) No(0)