What is the greatest possible positive integer n if 16^n divides (44)^44 without leaving a remainder

• (44)^44 = (4 × 11)^44 = (4^44) x (11^4) = ((4^2)^22) x (11^4) = (16^22) x (11^4). Therefore n=22. Answer
• 5 years agoHelpfull: Yes(5) No(4)
• please clearly tell me the solution for this que...
• 5 years agoHelpfull: Yes(2) No(0)
• 44^44=(2^88)*(11^44)
  16^n=2^(4n)
  n=22
• 5 years agoHelpfull: Yes(2) No(1)
• (44)^44=(4*11)^44
  =(4)^44*(11)^44
  =(2^2)^44*(11)^44
  =(2)^88*(11)^44.
  Now come to the denominator
  (2^4)^n
  =(2)^4n
  ie. ((2^88)*(11^44))/(2^4n)
  So,4n=88
  n=22
  Ans:22
• 2 years agoHelpfull: Yes(1) No(0)
• 2 is the possible positive integer
• 5 years agoHelpfull: Yes(0) No(4)