369^77/7

What is the remainder?

• 139^77/7
  => (7*20-1)^77/7
  => (-1)^77/7
  => -1/7 => rem = 6
• 10 years agoHelpfull: Yes(18) No(25)
• answer is 3,because for every 6 powers (7-1,I.e.,divisor -1) reminder is 1,so 77%7=5,
  
  so for 369%7=5
  5
  (369^2)%7=(5*5)%7=4
  
  369^3)%7=(4*5)%7= 6
  
  
  369^4)%7=(6*5)%7=2
  
  369^5)%7=(2*5)%7=3
  
  so for (369 ^ 5)%7 reminder is 3
  and if we observe for 369^6)%7 = 3*5)%7 =1 so if n is divisor for (n-1)the power reminder is 1
  you can check this for (135^77)%7, (76^77)%7
  
  so answer is 3
• 9 years agoHelpfull: Yes(16) No(0)
• 139^77/7= (53*7-2)/7
  so remainder = (-2)/7
  remainder= 5
• 10 years agoHelpfull: Yes(11) No(2)
• ans is 3
  
• 9 years agoHelpfull: Yes(6) No(0)
• According to rule of power cycle divide the power by four,here 77 is divided by 4 it gives 1 as remainder.last digit is 9.so 9^1 is 9,then divide 9/7= 2 remainder. so ans is 2.
• 10 years agoHelpfull: Yes(5) No(2)
• answer is 3,because for every 6 powers (7-1,I.e.,divisor -1) reminder is 1,so 77%7=5,
  
  so for 369%7=5
  5
  (369^2)%7=(5*5)%7=4
  
  369^3)%7=(4*5)%7= 6
  
  
  369^4)%7=(6*5)%7=2
  
  369^5)%7=(2*5)%7=3
  
  so for (369 ^ 5)%7 reminder is 3
  and if we observe for 369^6)%7 = 3*5)%7 =1 so if n is divisor for (n-1)the power reminder is 1
  you can check this for (135^77)%7, (76^77)%7
  
  so answer is 3
• 9 years agoHelpfull: Yes(5) No(0)
• For 139^77/7
  Rem=6
• 10 years agoHelpfull: Yes(4) No(1)
• 3 is the right answer
  (364+5)^77/7-->5^77/7-->5*(5^2)^38/7-->5*(21+4)^38/7-->5*2^76/7-->5*2*(7+1)^25/7-->10/7-->3
• 9 years agoHelpfull: Yes(4) No(0)
• 9^1/7=2
  9^2/7=4
  9^3/7=1
  9^4/7=2
  
  so,,77/3=2
  r=2,,ans 4
  
• 10 years agoHelpfull: Yes(3) No(2)
• Problem wasnt like this !
  it was 139^77/7
  
• 10 years agoHelpfull: Yes(2) No(0)
• (371-2)^77/7
  =-2^77/7
  =(-2^2*2^75)/7
  =(-4*8^15)/7
  =(-4*1^15)/7
  -4/7
  =7-4
  =3 (ans)
• 9 years agoHelpfull: Yes(2) No(0)
• 9^77/7=[(9^3)^25]*(9^2)/7=rem(1)*81/7=rem is 4
  ans is 4
• 9 years agoHelpfull: Yes(1) No(0)
• the cylicity of the last digit in 369 i.e of 9 is 2..
  then we devide 77/2 the remainder is 1..then the last digit of the no. 369^77
  is= 9^1=9 so the remainder is 9/7=2
• 9 years agoHelpfull: Yes(1) No(0)
• can any one tell me which is the correct answer 6 or 2
• 9 years agoHelpfull: Yes(0) No(0)
• Is 2 correct answer??
  
• 9 years agoHelpfull: Yes(0) No(0)
• question is not 139 guys....
  its 369....
• 9 years agoHelpfull: Yes(0) No(0)
• 369/7 gives the remainder is 5. now we have to simply calculate 5^77/7 to find the answer.
  again, 5^7/7 will give remainder 5. Similarly 5^11/7 will give remainder 3.
  So the remainder is 3.
  
• 9 years agoHelpfull: Yes(0) No(0)