3) What is the largest positive integer n for which 8^n divides 44^44?

• ans is 29....
  see akilesh
  8^n/44^44
  
  8^n=2^3n,44^44=(4*11)^44=(2^2*11)^44=2^88
  
  so,3n=88
  n=29(app)
  
• 11 years agoHelpfull: Yes(10) No(3)
• please explain
• 11 years agoHelpfull: Yes(9) No(0)
• 44^2 is devisible by 8.
  like that 44^4 by 8^2
  44^6 by 8^3.... and so on
  hence for 44 we have to take 22.
  hence n=22
  if it is rong den plz correct me.thnx
• 11 years agoHelpfull: Yes(7) No(2)
• 44^44/8^n
  =(2^2*44)*11^44/2^3n
  =2^(88-3n)*11^44
  now to make it devisible 88-3n=0
  n=29
• 11 years agoHelpfull: Yes(5) No(0)
• 44=4*11
  now
  4^44/8^n= 2^88/2^3n
  now (88/3) we get 29 is the closest integer
  so ans is 29
• 11 years agoHelpfull: Yes(1) No(0)
• 8^2= 4^3
  so ans is 28
• 11 years agoHelpfull: Yes(0) No(14)
• 44=2*2*11
  44^44/8^n=2^88*11^44/2^3n
  3n
• 11 years agoHelpfull: Yes(0) No(3)
• 44=2*2*11
  44^44/8^n=2^88*11^44/2^3n
  3n
• 11 years agoHelpfull: Yes(0) No(2)