What is the remainder when 6^17+117^6 is divided by 7?
A. 1
B. 6
C. 0
D. 3

• 1)6^17 mod 7
  (7-1)^17 mod 7
  (-1)^17 mod 7
  =-1
  
  2)117^6 mod 7
  (16*7+5)^6 mod 7
  (5)^6 mod 7
  (25)^3 mod 7
  (7*3+4)^3 mod 7
  (4)^3 mod 7
  64 mod 7
  =1
  6^17+117^6 is divided by 7 will be (1)+(2)
  -1+1=0
  remainder when 6^17+117^6 is divided by 7 will be 0(ans)
  C. 0 (ans)
• 12 years agoHelpfull: Yes(51) No(1)
• (7-1)^17 + (119-2)^6
  =7X-1 + 7Y+ 2^6 [x&y are constants]
  =7(X+Y)+63
  =7(X+Y+9)
  so rem is 0
• 12 years agoHelpfull: Yes(11) No(2)
• the answer is 1.
  6 to the power anything will always result ending with last digit at 6.
  now consider the next part.. 117 to the power 6 .. assume it to be xx7 to the power 6 ie just focus on 7 and 6... 7 to the power can be broken as 49*49*49 .. this will rsult in something ending with 9...
  now add the remainders of first and second part.. ie 6+9=15
  15%7=1... thats so simple
• 12 years agoHelpfull: Yes(5) No(15)
• consider unit digit power of this div by4 remainder of this is power of init digit so 6^1+7^2=55
  55/7=remain6
• 12 years agoHelpfull: Yes(2) No(3)
• 6793/7=256 and rem=1
  ans=1
• 12 years agoHelpfull: Yes(1) No(14)
• ans option may be B or C..
• 12 years agoHelpfull: Yes(1) No(3)
• yess..0 is d ans...got it..
• 12 years agoHelpfull: Yes(1) No(1)
• Solutoon is 0
• 9 years agoHelpfull: Yes(0) No(0)
• Solutoon is 0
• 9 years agoHelpfull: Yes(0) No(0)