76^77 / 7. what is the reminder

• 76^77 / 7
  =>(7*11-1)^77 / 7
  => (-1)^77/7
  => -1/7
  => 6/7 => remainder = 6
  
• 10 years agoHelpfull: Yes(19) No(1)
• 76^77/7 ==> [76*76*76....upto 77times]/7
  
  76^1/7=6 [remainder(6) wen v divide 76/7]
  
  Therefore [6*6*6*....upto 77times]/7
  
  use cyclic remainder theory
  
  6^1/7= 6
  6^2/7= 36/7= 1
  6^3/7= 216/7= 6
  6^4/7= 1296/7= 1
  so it follows like 6,1,6,1
  
  we ll get d remainder as 6 for all odd powers of 6 nd 1 for all d even power of 6
  
  so 76^77 which has an odd power
  so the remainder ll be 6
• 10 years agoHelpfull: Yes(11) No(0)
• 6...since 76^77= -1^77= -1 so ans will be 6
• 10 years agoHelpfull: Yes(1) No(0)
• as we know,the remainder of 6^anything is 6.hence the ans will b 6 as the unit digit of 76 is 6.
• 9 years agoHelpfull: Yes(1) No(0)
• cycle of 6 always leave 6 in the LSB
  so,76^77 leaves 6 in the LSB so,6/7 will give remainder=6
• 10 years agoHelpfull: Yes(0) No(0)
• ans is 6.
  
• 9 years agoHelpfull: Yes(0) No(1)
• in 76 ---- the unit digit is 6^77 is always 6
  so 6/7 reminder is 6 only
• 9 years agoHelpfull: Yes(0) No(0)
• answer is 6
• 9 years agoHelpfull: Yes(0) No(0)
• 6 is the remainder
• 9 years agoHelpfull: Yes(0) No(0)
• 76 have 6 at unit place
  so 6^77 will have 6 at unit place
  thus 6/7=6
  (since 6 appears at unit place as many no. of times you multiply)
• 9 years agoHelpfull: Yes(0) No(0)