Find the reminder when 50^51^52 is divided with 11

• use reminder theorem. here it is given as 50^51^52. but consider it as 50*51*52 so when it is divided by 11 it gives -ve remainder of (-5)*(-4)*(-3) = 20*(-3) again use remainder theorem so now it becomes (-2)*(-3) = 6. so the ans is 6. But note that it is valid only in case of consecutive no. i.e 50,51,52 or 34,35,36 but not in case when it is given 30^72^87 etc
  
  
  
• 10 years agoHelpfull: Yes(63) No(17)
• 6 is the reminder
• 10 years agoHelpfull: Yes(18) No(5)
• 3 is the remainder.
  50^2652
  (44+6)^2652/11
  6^2652/11
  36^1326/11
  (33+3)^1326/11
  3^1326/11
  .........
  ........
  ........
  -8/11
  3
• 10 years agoHelpfull: Yes(10) No(15)
• 50^51^52/11 can be written as 50^N/11=6^N/11(As remainder is 6 when 50 is divided by 11).
  =Remainder
  6^1/11=6
  6^2/11=3
  6^3/11=7
  6^4/11=9
  6^5/11=8
  6^6/11=4
  6^7/11=2
  6^8/11=1
  i.e in cycle of 8 we get 1 as a remainder.
  Again,
  N/8=51^52/8=3^52/8
  again find the remainder as above way
  3^1/8=3
  3^2/8=1
  cycle is 2
  i.e 52/2=0 remainder means we take last term of a cycle i.e:3^2/8=1.
  so here the remainder is 1.
  Now this(remainder 1) means take the 1st term of the cycle 6 i.e;6^1/11=6. as a final remainder.
  therefore 50^51^52/11=6(Answer)
  
• 9 years agoHelpfull: Yes(8) No(3)
• : Fermat little theorem says, a^p−1/p remainder is 1.
  ie., 30^10 or 8^10when divided by 11 remainder is 1.
  The unit digit of 51^52 is 1 (using cyclicity of unit digits) Click here
  
  So 51^52 = 10K + 1
  50^(10K+1) %11=(50^10)K.50^1%11=3^5.k*6%11
  so, 45*6%11=1.6=6
  so rem =6. where 10 = phi(11)=(1-1/11)*11
• 10 years agoHelpfull: Yes(6) No(2)
• 3 will be the answer
• 10 years agoHelpfull: Yes(5) No(13)
• the answer will be 6 because 50 and 11 are coprime to each other so by euler thoerem, we can find out the euler no. of 11 , since it is prime no. the euler no. of 11 will be 10 , so divide the power of 50 by 10 then we will get remainder as 1
  now we r left with 50^1/11 so when we divide 50^1 by 11 we will get the remainder as "6".
• 10 years agoHelpfull: Yes(4) No(1)
• 6 will be the correct answer because 51^52 will give unit digit as 1.
  Therefore, When 50^1 is divided by 11 will give a remainder 6
  
• 10 years agoHelpfull: Yes(2) No(8)
• 6 because 50 divided by 11 gives 6 remainder
• 10 years agoHelpfull: Yes(2) No(8)
• Just check the inter most no. Here 50 find the remainder that will be the result because as many times u power it factors will be same...check for any small,value the answer will always be the same depending on the central number.so,ans will be 6. @s 50/11 gives 6 as remainder
• 10 years agoHelpfull: Yes(2) No(0)
• 50 power 51*52 = 50 power 2652 => 50 power 2652 => 50 power 2650 will exaclty divided by 11 and remaining 2500/11 gives remainder is 3
• 10 years agoHelpfull: Yes(1) No(1)
• answer is 3
• 9 years agoHelpfull: Yes(1) No(2)
• if expression is like 50^(51^52) then remainder is 6.
  BUT if expression is like (50^51)^52 OR you can say 50^2652 then remainder is 3.
  
• 9 years agoHelpfull: Yes(1) No(0)
• reminder will be 3.
  whoever getting the answer apart from 3 please do proper calculation.
• 9 years agoHelpfull: Yes(1) No(2)
• reminder= 3
  
• 8 years agoHelpfull: Yes(1) No(0)
• 50^51^52/11==(50^50^52)50/11
  SO, 11)((50^50^52)*50)(4
  44
  --------------------
  06
• 10 years agoHelpfull: Yes(0) No(1)
• 6 is the correct answer
• 10 years agoHelpfull: Yes(0) No(0)
• Ans is 6.
  where phi(11)=(1-1/11)*11=10
  => 50^10k = 1mod11
  So 51^52 is to be written in the form of 10k + a.
  Now unit digit of 5152 = 1 => 5152 = 10k + 1.
  => 5051^52 = 50(10k + 1) = 50mod11 = 6 mod11
• 10 years agoHelpfull: Yes(0) No(2)
• using cyclicity of unit digits 51^52=51^0=1=50^10k+1 [cyclicity of 1 is 1 & 52/1 gives reminder 0].
  Fermat little theorem says, a^ (p−1)/ p remainder is 1. therefore
  50^(10k+1)/11= ((50^10)^k . 50^1)/11
  = 50/11=rim 6
• 9 years agoHelpfull: Yes(0) No(2)
• In these typ que...
  1. 50 %11 =6
  2.now eq will be 6^51^52 divide 11'
  3. now try to get no. of 6 for which we can get 1 reminder after divide 11 here let see
  6*6/11 gives 3 reminder
  6*3/11 gives 7 rem
  7*6/11 gives 9
  9*6/11 gives 10
  10*6/11 gives 5
  5*6/11 gives 8
  8*6/11 gives 4
  4*6/11 gives 2
  "2*6/11 gives 1 " thats situation we want .... upto these we have used 10 sixes.......
  4. now we can write eq like that.............
  now 51 =10*5+1
  so 6^(50+1)^52 /11
  6^(10*5+1)^52/11
  in these situation we know 6^10/11 will give 1 remainder so 6^50/11 will also give 1 remainder so 6^51^52 will give 1 reminder now remaining
  6^1^52/11 and you know 1^52 always gives 1 so now eq will be
  6^1/11=6 reaminder ans...................
• 8 years agoHelpfull: Yes(0) No(0)
• STEP(1) 52 is deivided by 4 =means no remainder
  STEP(2) 51 is devided by 10= 1 as remainder
  STEP(3) 50 is devided by 11= 6 as remainder
  
  now combining all in equation= 6^1^0= 6 will be the answer
• 8 years agoHelpfull: Yes(0) No(0)