48 ^ 567 /7. What is the remainder?

• 48 ^ 567 / 7
  
  = (7*7-1)^567 / 7
  
  = (-1)^567 / 7
  
  = -1/7
  
  rem = 7-1 = 6
• 9 years agoHelpfull: Yes(33) No(1)
• 6 ans.
  48^567=(7*7-1)^567
  7*7 is multiple of 7 so won't give remainder.
  (-1)^567=-1
  so -1/7 remainder is -1 or 6
• 9 years agoHelpfull: Yes(17) No(4)
• correction to my previous answer.
  remainder is 6.
  (7*7 -1)^ 567 /7
  leaves remainder -1 . but as remainder is always positive. we have to add 7 to negative value. hence remainder = 7 + (-1) = 6
• 9 years agoHelpfull: Yes(5) No(0)
• 6 is final ans. no doubt
• 9 years agoHelpfull: Yes(4) No(0)
• remainder is 1.
  (7*7 - 1)^567 / 7
• 9 years agoHelpfull: Yes(3) No(5)
• 
  (48^3)189
  8^3=2
  2%7=2
  2 is the remainder
  
• 9 years agoHelpfull: Yes(2) No(5)
• 48...48(567 times)/7 remainder =6...6(567 times)/7 remainder =36...36(283 times).6/7 remainder =1.1...(283 times).6/7 remainder =6
• 9 years agoHelpfull: Yes(2) No(0)
• 567%8=7
  8^7=2(cyclicity)
  2%7=2
  hence, remainder=2.
• 9 years agoHelpfull: Yes(2) No(4)
• 48^1 / 7 = Rem = 6 ,
  48^2 / 7 = Rem = 1 ,
  48^3 / 7 = Rem = 6 ,
  48^4 / 7 = Rem = 1,
  6,1 forms a cycle ... i.e , we infer 48^odd / 7 = Rem = 6 and that for even is 1 . hence Ans is 6
• 9 years agoHelpfull: Yes(2) No(0)
• 48^567 hence
  8^7=2(based on cyclicity)
  2%7=2
  hence the remainder is 2
• 9 years agoHelpfull: Yes(1) No(5)
• 48/7 remainder is 6.
  since (6/7)^567=-1.
  (-1/7)^567= -1/7 = 7-1/7 = 6/7 = 6...
  Ans is 6....
• 9 years agoHelpfull: Yes(1) No(0)
• R(48^567/7)
  
  cyclicity of 8 is 8 4 2 6
  R(567/4)=3, the position of 3 is 2.
  so the remainder is 2
  
• 9 years agoHelpfull: Yes(1) No(1)
• ans is :6 by using remainder theorem
  consider 48/7.then (48+1)/7 is divisible by 7.so,by remainder theorem
  7-1=6.
  hence ans is 6
  
• 9 years agoHelpfull: Yes(1) No(0)
• ans-6
  48^567/7=6^567/7=(-1)^567/7=-1/7=6(negative reminder concept)
• 9 years agoHelpfull: Yes(0) No(0)
• 48^567/7
  7*7=49,so 49is the multiple of 7
  so we have to add one to the given number 48,so 48+1=49
  here the unit digit of given power is 7,7 is the odd num,so we have to put -1
  (-1)^567/7
  -1/7
  7-1=6
  6 is the ans.
  
• 9 years agoHelpfull: Yes(0) No(0)
• cycle of 8 are 8 4 2 6
  567/4=3
  power=567,no of cycles=4.remainder=3.
  power of 1=8
  power of 2=4
  power of 3=2
  power of 0=6
  so remainder is 2
• 9 years agoHelpfull: Yes(0) No(0)
• guys 2 or 6 is the answer ????finally
• 9 years agoHelpfull: Yes(0) No(0)
• 6 is the remainder as per the negative remainder concept
  48^567/7=(-1)^567/7=(-1)/7=7-1=6
• 9 years agoHelpfull: Yes(0) No(0)
• 48=12*2=2^4(567)*3^2(567)=2^2268*3^1701=349371267/7=remainder is 0
• 9 years agoHelpfull: Yes(0) No(0)
• 48/7=6
  we get 6 as remainder
• 9 years agoHelpfull: Yes(0) No(0)
• -1
  (49-1)^567 all the terms expect last digit is divisible by 7 these last digit (-1)^567 is the remainder
  
• 9 years agoHelpfull: Yes(0) No(0)
• Remainder for 48^567/7 is same as remainder for 6^567/7
  possible remainders: 6^1/7 = 6
  6^2/7 = 1 and continues..
  No of possible remainders = 2
  567/2 remainder = 1 i.e., first possibility which is = 6 (ans)
• 9 years agoHelpfull: Yes(0) No(0)
• euler no of 7=6
  567%6=3
  48^3/7=48*48*48%7=-1*-1*-1=-1
  7-1=6
  ans=6
• 9 years agoHelpfull: Yes(0) No(0)
• i chkd it out in several books..by remainder theorem it has to be solved..thus it is-
  48=(7*7-1)
  so,48^567=(7*7-1)^567
  by binomial expansion it is,(7*7)^567 which is exactly divisible by 7.
  so the remainder is,(-1)^567=-1
  so by negative remainder concept,the final rem. is 7-1=6
  
• 9 years agoHelpfull: Yes(0) No(0)
• what is the remainder when 48^565 divided by 7? todays my tcs question
• 9 years agoHelpfull: Yes(0) No(0)
• (6)^567/7
  6^1%7=6
  6^2%7=1
  567/2 =1
  1st term of cycle i.e. 6
  
• 9 years agoHelpfull: Yes(0) No(0)
• consider, 567%4,remainder=3
  now, 48^3.. remainder=6..
  hence 6 is the right answer..
• 9 years agoHelpfull: Yes(0) No(0)
• 6
  as 49 is divisle by 7
  48 will have -1 remainder for odd number times of multiple we should add it to 7
  for even times of multile we simply write 1
• 6 years agoHelpfull: Yes(0) No(0)