2^81 when divided by 6,what is the remainder

• 2^81/6 ====> (2^1*2^2*2^3*....81 times]/6
  
  2^1/6 ----------> remainder=2
  2^2/6 -->4/6 ---> remainder=4
  2^3/6 -->8/6 ---> remainder=2
  2^4/6 -->16/6 --->remainder=4
  2^5/6 -->32/6 --->remainder=2
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  it goes on in a cyclic manner
  
  so remainder is "2" for all odd powers of 2 nd "4" for all even powers of 2
  
  here 2^81 which has the odd power
  
  so remainder =2
• 10 years agoHelpfull: Yes(60) No(1)
• ((2^3)^27)/6
  ==>((8)^27)/6
  ==>(2^27)/6
  ==>((8)^9)/6
  ==>(2^9)/6
  ==>((8)^3)/6
  ==>(2^3)/6
  ==>8/6
  
  so remainder is 2
• 10 years agoHelpfull: Yes(13) No(2)
• 2^odd/6------->remainder= 2.
  2^even/6------>remainder= 4.
  
  So, the answer is 2.
• 10 years agoHelpfull: Yes(6) No(0)
• remainder= 1
  
  proof:
  2^81/6
  = 4^80/6
  =2^79/3
  =2^(4+75)/3
  =16^75/3...
  & 3|16|5
  15
  ----
  1
  
  since 16^n/3, remainder=1
  16^75/3, remainder=1
  
  hence proved...
  
• 10 years agoHelpfull: Yes(2) No(8)
• 2^81=2^80*2^1
  so 2^80*2/6=2^8*10/3
  now just take 2^8/3=256/3
  which leaves a reminder of 1..so 1 is the ans
• 10 years agoHelpfull: Yes(2) No(3)
• Ans: 1 ;(2^81)/(3x2)==>(2^80)/3==>even powers will give remainer 1 and odd powers will give remainder 2
• 10 years agoHelpfull: Yes(2) No(0)
• 2^81/(2*3)
  =2^80/3
  =(3-1)^80/3
  =(-1)^80
  =1
• 10 years agoHelpfull: Yes(1) No(2)
• let odd power of 2 is 3=8
  8%6=2
  next power 5=2^5=32
  32%6=2
  odd power of 2 when divided by 6 remainder is 2
• 10 years agoHelpfull: Yes(1) No(0)
• 2^81===2*4^40 =16^20*2/6 =rem2*4^20/6 2*16^10/6 =2*4^5/6 =8*16^2/6=2*4/6=2
• 10 years agoHelpfull: Yes(1) No(0)
• for every 4 divisivbles we get 2 so
  for 81 th number we get 2 so it is divide at 0 we get remainder as 2
  
• 10 years agoHelpfull: Yes(1) No(0)
• 2^81
  2 s unit sequence 2,4,6,8,0 so totally 5
  81/5= 16 quot, 1 remaindr
  in sequence list 1 ll be 2
  so ans=2
• 10 years agoHelpfull: Yes(1) No(0)
• 4 is the answer...
• 10 years agoHelpfull: Yes(0) No(5)
• 2^81/6
  ->2^9/6=1
  ->2^9/6,2^9/6. . . . .2^9/6 total 9 times each one gives remainder one
  so final remainder is 1
  
• 10 years agoHelpfull: Yes(0) No(4)