Find the remainder when 6^50 is divided by 215?

• 6^1 --> 6%215=6
  6^2 --->36%215=36
  6^3 -->216%215=1
  6^4 --->1296%215 =6 so again remainders are repeating so stop at 6^3 and total count is 3
  now in (6^50) ---> 50 % 3= 2 so checking remainder at 2nd one i.e 6^2 gives the answer i.e 36...
  JUS ANALYSE THIS ...IT IS VERY EASY....
• 8 years agoHelpfull: Yes(15) No(0)
• 6^(3*16)*6^2/215=( 216^16)*36/215=36/215=36
• 8 years agoHelpfull: Yes(7) No(0)
• 6^50=6^45*6^5
  =(215+1)^15*6^5
  the 1st term and the 2nd term of (215+1)^15 always divided by 215 only 1 remain .
  so u have to evaluate the remainder of 6^5/215 which is equal to 36
  so ans is 36
• 8 years agoHelpfull: Yes(4) No(0)
• 650=(6^3)^16.6^2=216^16.6^2
  =36
• 8 years agoHelpfull: Yes(4) No(1)
• ((6^3)^16*36)/215=216^16*36/215=(215+1)^16*36/215=36/215,remainder=36
• 8 years agoHelpfull: Yes(2) No(0)
• 6^50/215=6^50/6^3-1
  =>6^2*6^48/6^3-1
  =>6^2*(6^3)^16/6^3-1
  =>6^2*(1)^16=36
• 8 years agoHelpfull: Yes(2) No(0)
• The expression can be written as (6^3)^16*6^2/215
  36/216 = rem 36
• 8 years agoHelpfull: Yes(2) No(0)
• (215+1)^16*36/215
  1*3/215
  =36
• 8 years agoHelpfull: Yes(2) No(0)
• Reminder will be 1
• 8 years agoHelpfull: Yes(2) No(0)
• 6 or 1, because the unit digit of 215 multiples are 5 and 0. when subtract the 6 with 5 or 0, the answer will be 1 or 6.
• 8 years agoHelpfull: Yes(0) No(1)
• 6^50/215=(36*(216)^12)/215=36
• 8 years agoHelpfull: Yes(0) No(0)