find remainder 4^5^6^7+1/10

• the question becones 4^210+1/10.
  now 1/10 always gives 1 as remainder. keep it separate.
  now 4^210=16^105 =(10 +6)^105 when divided by 10 given remainder as 6^105 whose last digit is always 6. so atlast remainder would be 6. and 1 we have before.thus answer is 7.
• 11 years agoHelpfull: Yes(25) No(7)
• 5
  4^5^anythning means 4^odd ie remainder 4. so 4+1= 5(Ans)
• 11 years agoHelpfull: Yes(21) No(3)
• for every number the cycle of 4 will be always repeating
  Eg: 2^1=2 3^1=3 4^1=4 5^1=5
  2^2=4 3^2=9 4^2=6 5^2=0
  2^3=8 3^3=7 4^3=4 5^3=5
  2^4=6 3^4=1 4^4=6 5^4=0 .....................
  so we can easily answer when divided by 10
  the given data is (4^210)+1/10
  now 210 can be written as 4*52+2
  therefore 52 times the cycle repeats so we need not calculate,
  +2 gives the value of 4^2=6
  now 6+1/10=7/10=7
  so,7 is the answer
  (same funda will be used to find the unit's place)
• 11 years agoHelpfull: Yes(6) No(2)
• ans will be 1
• 11 years agoHelpfull: Yes(4) No(3)
• answer is 7.
  (4^210+1)/10 remainder is 7.
• 11 years agoHelpfull: Yes(4) No(2)
• ans is 7
  4^5=4
  4^6=6
  6^7=6
  6+1/10
  7
• 11 years agoHelpfull: Yes(4) No(1)
• 7 ans
  4^5^6^7/10=6
  1/10=1
  ans 7
• 11 years agoHelpfull: Yes(2) No(2)
• 7
  
  
  
  
  
  
  
• 11 years agoHelpfull: Yes(1) No(3)
• your solution is very clear @kanuru sreesatya
• 11 years agoHelpfull: Yes(1) No(0)
• i think he didnt gave ad 4^(5*6*7) but as 4^5^6^7 @gaurav@kanuru @durgesh
  pls xpln clearly...
• 11 years agoHelpfull: Yes(1) No(0)
• 4^any odd no. =4 in unit digit*10=40, 40+1/10, so remainder is 1
• 11 years agoHelpfull: Yes(0) No(2)