find the remainder when
3^2014 divided by 60

• (3*3*3*3)^503 *3^2/60
  21^503 *9/60
  but 21^2=441 and 441/60 gives remainder 21
  therefore 21^503/60 gives remainder 21
  so 21*9/60=189/60
  remainder will be 9
  ans=9
• 9 years agoHelpfull: Yes(2) No(2)
• 81^503 gives the remainder 21 And 2 gives a remainder of 2 only when divided by 60. Hence the remainder when 3^2014 is divided by 60 is the remainder when the product 21 × 2 is divided by 60.
  
  Answer = 42
• 9 years agoHelpfull: Yes(0) No(0)
• @junaid ahmed khan thanks for giving the solution
  
• 9 years agoHelpfull: Yes(0) No(0)
• (3)^2014=(3^4)^503*3^2
  using reminder rule 3^1 gives 3 (as unit place)
  3^2 gives 9 (AS unit place)
  3^3 gives 7 (as unit place)
  3^4 gives 1 (as unit place)
  hence, the repetition is followed next.
  hence after solving it gives unit place 9
  and when dividing it by 60 it gives 9 as reminder
• 9 years agoHelpfull: Yes(0) No(0)