What is the greatest possible positive integer n if 8^n divides (44)^44 without leaving a remainder?
a)14 b)28 c)29 d)15

• 44^44 = 2^88 *11^44
  = 8^29 * 2 * 11^44
  so ans is 29
• 12 years agoHelpfull: Yes(62) No(14)
• 8^n=(2^3)^n
  44^44=(11*2^2)^44=11^44*2^88
  (11^44 *2^88)/ 2^3n
  3n=88
  n=29
• 12 years agoHelpfull: Yes(46) No(9)
• VISHNU PRIYA plz tell me why u write 3n=88 can any budy explain me
• 12 years agoHelpfull: Yes(11) No(5)
• 8^n/(44^44)
  8^n=(2^3)^n
  (44^44)=(11*2^2)^44=(11^44)*(2^88)
  (11^44*2^88)/(2^3)^n=(11^44)*(2^88)/(2^3n)
  Here 3n=88,n=29. Hence ans will be 29 bcoz 29 is the greatest possible positive integer without leaving remainder.
  
  
• 12 years agoHelpfull: Yes(7) No(7)
• (11*4)^44/(4*2)^n,,so max value of n from option is coming 28..plz check
• 12 years agoHelpfull: Yes(2) No(4)
• every 44^2 is divided by 8 and gives output that is 2421 not divisible by 8 hence the answer should be 15.
• 12 years agoHelpfull: Yes(2) No(12)
• 44^odd=last digit is 4 44^even last digit 6............
  now 8^1=8
  8^2=4
  8^3=2
  8^4=6
  8^5= again last digit will 8 so in this way we can see 44^44 last digit is 6 and from options we can see max value of n is 28 where it gives the last digit 6..... so 28 is correct.......
• 12 years agoHelpfull: Yes(2) No(7)
• (44*44*44)/(8*8)=11*11*11 i.e. with no remainder
  there is 44th time 44 and think as in grp of three maximum 14 times 44 divisible by two 8....so 14*2=28...is answer...pls confirm.. ;)
• 12 years agoHelpfull: Yes(1) No(9)
• answer is d) 15
  reason-
  because when we divide 44^2 by 8 there is no remainder
  as it is 44^44 we can make 8^22 to have no remainder because as there is 44 times 44 and 2 times 44 is needed to be divisible by 8 so we need 22 times 8 to be divisible by 44^44
  but in the option 22 is not there the number less than 22 in the option is 15 so the answer is 15
• 11 years agoHelpfull: Yes(1) No(5)
• @HARSH PODDAR akhono answer korar age hoyni tr..vulval answer krbi na bkcd
  
• 11 years agoHelpfull: Yes(1) No(1)
• Hello Guys hope u r doing well
  8^n divides 44^44
  so, (11*4)^44=11^44 and 4^44
  11^44 unit digit is 1
  4^44 unit digit is 6
  so 44^44 unit digit is 6
  if we take 8^28 whose unit digit is 6 then obviously 6%6 is 0.
  So I think ans is 28
• 5 years agoHelpfull: Yes(1) No(1)
• ans=28.
  because 44^44 and every 4^even digit divisible by 8 so maximum 8^28
• 12 years agoHelpfull: Yes(0) No(7)