what is the remainder when 4^29 is divided by 63?
a)16
b)12
c)61
d)none of these.

• as 4^3 is 64 so when devided by 63 we get remainder 1 .. So 4^27 rmainder is 1 4^2 is 16 so the remainder is 16.. so the net remainder is 16
• 9 years agoHelpfull: Yes(4) No(1)
• 16*64*64*64*64*64*64*64*64*64
  .............................................................
  63
  from negative remainder method.
  (64-63=1) that is 9 times one.
  so.
  16*1*1*1*1*1*1*1*1*1
  ........................................
  63
  so the remainder is 16.
  OPTION (A).
  
• 9 years agoHelpfull: Yes(3) No(0)
• As it's given,
  4^29 mod 63 = (4^2)*(4^27) mod 63 = 16*(4^3)^9 mod 63 = 16*(64)^9 mod 63
  so,above expression can be written as,
  =16*(63+1)^9 mod 63
  now, 63^9 would give remainder 0,when divided by 63
  therefore, 16*(1)^9 mod 63 can only be considered
  1^9 = 1
  so, 16 mod 63 = 16
  hence,the answer is 16.
• 9 years agoHelpfull: Yes(3) No(1)
• 4^2 * 4^3 * 4^3 *4^ 3* 4^3 * 4^3 *4^ 3*4^ 3*4^ 3*4^ 3
  =16*4^3 *64*64*64*64*64*64*64*64/63-----(1)
  take one 64 from the above
  64/63=1(remainder) and so on we get eight ones as remainders for 63
  and 16*64/63=1024/63=16(remainder)
  note:if we talke 4^3=64 in equ (1) we get 16/63 =which is not possible
• 9 years agoHelpfull: Yes(1) No(0)
• (4^3)^9*4^2/63
  4^3/63 remainder is 1
  4^2/63
  so remainder is 16
  
  
• 9 years agoHelpfull: Yes(1) No(0)
• 4^29=64^9x16
  when divided by 63 give remainder 1^9x16=16
  so a)16 is correct
• 9 years agoHelpfull: Yes(0) No(0)
• 4^29/63=((4^3)^9 * 4^2 )/63 ( when 4^3=64 divided by 63 we get remainder as 1 , when we divide
  = (1)^9 * 16 4^2=16 with 63 we get remainder as 16 )
  =16
• 9 years agoHelpfull: Yes(0) No(0)
• The ans is 16
• 9 years agoHelpfull: Yes(0) No(1)
• 16*64*64*64*64*64*64*64*64*64
  .............................................................
  63
  from negative remainder method.
  (64-63=1) that is 9 times one.
  so.
  16*1*1*1*1*1*1*1*1*1
  ........................................
  63
  so the remainder is 16.
  OPTION (A).
  
• 9 years agoHelpfull: Yes(0) No(0)
• 4^29= [ (4^3)^9 *4^2 ] /63
  = 1^9 *16/ 63
  =16 reminder
• 9 years agoHelpfull: Yes(0) No(0)
• 4^29/63= 4^2*4^27/63= 4^27/63=1 and 4^2 /63= 16 . hence ans is 16.
• 9 years agoHelpfull: Yes(0) No(0)
• when 64/63 gives remainder 1, so in every 2^6 the remainder will be 1.
  4^29= 2^58
  the closest factor of 6 is 54 so we have to check only for 2^(58-54) i. e. 16
  because 2^54 will give remainder 1.
  I hope it helped.
• 8 years agoHelpfull: Yes(0) No(0)
• ((4^3)^9 *4^2)/63
  ((1)^9*16)/63
  16/63
  so 16
  
• 8 years agoHelpfull: Yes(0) No(0)
• none of these
• 6 years agoHelpfull: Yes(0) No(0)