what is the remainder when 48^565 divided by 7?

• ans will be 6....
  
  as (ax-1)^n/a..format if n is odd thn remainder will be a-1
  
  so (7*7-1)^565/7 will give 7-1=6 as remainder
• 10 years agoHelpfull: Yes(14) No(5)
• 48/7= remainder is -1
  ((-1)^565)+7= 6 ans..
• 10 years agoHelpfull: Yes(10) No(3)
• 48^565= 6^(565)
  
  Now
  6^564 X 6
  => 36^282 X 6
  => 1^282 X 6= 6
  Hence remainder is 6
• 10 years agoHelpfull: Yes(3) No(5)
• Ankit could you plz explain me why are you taking 6^565?
• 10 years agoHelpfull: Yes(2) No(0)
• 6
  48/7=6 remainder
• 10 years agoHelpfull: Yes(2) No(1)
• (7*6+6)^565
  6^565
  6^1%7=6
  6^2%7=1
  6^3%7=6
  6^4%7=1
  .
  .
  .
  ((6^2)^284+6)%7=(1+6)%7=0
  So the Answer is 0
• 10 years agoHelpfull: Yes(1) No(3)
• By using formula:(ax-1)^n/a if n is even remainder 1;
  if ni is odd remainder n-1;
  i.e. (7*7-)^565/7;reminder=6
  
  
• 10 years agoHelpfull: Yes(1) No(1)
• 48^565/7=(7*7-1)^565/7=(-1)^565/7
  remainder=7-1=6
• 10 years agoHelpfull: Yes(1) No(1)
• @Farheen.. 48/7 means= (42+6)/7
  Since 42 is divisible by 7 we consider only 6. Clear??
• 10 years agoHelpfull: Yes(1) No(3)
• (48^565)%7
  =(6^565)%7 (48/7 FIND REMAINDER)
  FORMULA (ax-1)^n >> remainder=1 when n is evev
  =-1 n odd
  here -1 >> = 6
• 10 years agoHelpfull: Yes(1) No(2)
• 48/7 gives 6
  ans=6
• 10 years agoHelpfull: Yes(1) No(0)
• (7*6+6)^565
  = 6^564+1= (6^2)282*6
  => 36/7 =1
  1^282) *6
  1*6 = 6/7 = 6
• 10 years agoHelpfull: Yes(1) No(1)
• consider (8^564*8^1)/7 this certainly give you six
• 10 years agoHelpfull: Yes(1) No(0)
• only remainder responsible for remainder so 48/7 then remainder is -1 so
  (-1)^565 = -1 then 1/7 remainder is 6
• 10 years agoHelpfull: Yes(0) No(3)
• 48=7*7-1
  (-1)^565=-1
  rem=7-1=6
• 10 years agoHelpfull: Yes(0) No(1)
• 48/7
  rem=6
• 10 years agoHelpfull: Yes(0) No(3)
• 48/7. reminder =6 then 6^565 =6 because 6^nth power have unit digit 6... so ans is 6
  note: 6^n=6, 4^n : n->even power means =unit digit 6
  odd power means =unit digit 4 always
• 10 years agoHelpfull: Yes(0) No(0)
• 2
  48^565/7
  48*48*48*......*48(565 times)/7
  now, 48/7 give rmindr=6
  so, for all 48 it will give 6 as rmindr
  now, 6*565/7=3390/7 whc gv rmindr 2
  so, ans=2
  
  
• 10 years agoHelpfull: Yes(0) No(0)
• Answer is 6
  Sol: (42+6)^565 / 7=> 42K+ 6^565/ 7
  now 42k/7 remainder is 0 and 6^565/7 remainder is 6
  ( (a^n / a+1) remainder is a if n=odd number)
• 9 years agoHelpfull: Yes(0) No(0)
• 48^565/7
  =(7*48^565)/49
  as rem(48^565/49)=-1
  hence remainder = (-1*7+7)
  =0
• 7 years agoHelpfull: Yes(0) No(0)