if 8^25 divided by 7 then what is reminder
a]25
b]1
c]0
d].....

• 8^25/7
  
  8 can be written as 7*1+1
  
  (7*1+1)^25/7
  (ax+1)^n/a always gives the remainder 1
  here a=7,x=1,n=25
  Hence remainder is 1
  
  Ans : 1
  
  
• 10 years agoHelpfull: Yes(59) No(0)
• 8^1 = 8
  8^2 = 4
  8^3 = 2
  8^4 = 6
  this pattern contiues 8,4,2,6 8,4,2,6
  8^25 = 8. 8 when divided by 7 gives remainder 1
  answer is b
• 10 years agoHelpfull: Yes(13) No(0)
• We can use cyclic remainder theorem
  8^1 % 7 = 1
  8^2 % 7 = 1
  8^3 % 5 = 1
  8^4 % 5 = 1
  .
  .
  .
  Again
  8^n % 7 = 1
  So the 1st cycle is upto the power of "4"...
  So the remainder of 8^35 % 8 will be (4k + n)th value...
  25 => 4*6+1 [k=6, n=1]
  If n=1, rem=1
  If n=2, rem=1
  If n=3, rem=1
  If n=4, rem=1
  Hence the remainder is 1
  
  Ans : 1
  
• 10 years agoHelpfull: Yes(7) No(0)
• if (a+1)^n/a then remainder is always 1
• 10 years agoHelpfull: Yes(4) No(0)
• 8^25 = 2^75
  2,4,8,16,32,64,128,256,512,... are powers of 2. Starting with
  power remainder
  2^3 1
  2^4 2
  2^5 4
  2^6 1
  hence for power 3,6,9,12..... remainder is 1.
  whenever 2^3n is divided by 7.. remainder is 1.
• 10 years agoHelpfull: Yes(4) No(0)
• We can use cyclic remainder theorem
  8^1 % 7 = 1
  8^2 % 7 = 1
  8^3 % 7 = 1
  8^4 % 7 = 1
  .
  .
  .
  Again
  8^n % 7 = 1
  So the 1st cycle is upto the power of "4"...
  So the remainder of 8^25 % 7 will be (4k + n)th value...
  25 => 4*6+1 [k=6, n=1]
  If n=1, rem=1
  If n=2, rem=1
  If n=3, rem=1
  If n=4, rem=1
  Hence the remainder is 1
  
  Ans : 1
  
• 10 years agoHelpfull: Yes(3) No(4)
• we know that
  (a+1)^n/a will always give 1 as remainder for all natural no of a and n.
  so ans=1
  (7+1)^25/7=1
• 10 years agoHelpfull: Yes(0) No(0)
• ans:
  since 8/7=1(rem)
  64/7=1(rem)
  512/7=1(rem)
  :
  :
  8^25=1(rem)
• 10 years agoHelpfull: Yes(0) No(0)
• option (b) is correct
  8^25/7=1^25/7=1/25
  so if 1 divided by 7 then rem=1
• 10 years agoHelpfull: Yes(0) No(0)
• by formula 8^25/7=(7+1)^25/7=1
• 10 years agoHelpfull: Yes(0) No(0)
• ans=1
  8^1/7=remainder=1
  8^2/7=remainder=1
  8^3/7=remainder=1
  so 8^25/7=remainder=1
  
• 10 years agoHelpfull: Yes(0) No(0)
• 25/4 here 7 cylicity is 4 hence remainder is 1
• 8 years agoHelpfull: Yes(0) No(0)
• Here reminder is. 1
• 6 years agoHelpfull: Yes(0) No(0)