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

• no positive integer value of n will satisfy given condition as zero is not a positive integer.
• 11 years agoHelpfull: Yes(20) No(3)
• kripaya aapas me maa behan naa khele
• 10 years agoHelpfull: Yes(7) No(2)
• no digit satisifies this condition because
  on dividing 44^n by 3 , we get remainders 2,1,2,1,2,....
  so, for no value, 44^44 % 3^n =0
• 11 years agoHelpfull: Yes(6) No(0)
• unit digit in 44^44 is 6. so largest value of n=2
• 11 years agoHelpfull: Yes(2) No(23)
• Ans will be definetly: n = 0
  The digit sum of 44 44 is when remainder obtained 44 44 divided by 9
  44 44 = (45−1) 44
  Each term is a multiple of 9 but the last term which is (−1) 44 = 1
  So the digit sum of 44 44 is 1.
  
  Now the divisibility rule for 3, 9, 27... is the sum of the digits should be divisible by 3, 9, 27 respectively. In each case the digit sum is either multiple of 3 or 9.
  So for any value of n > 1, the given expression is not divisible by 3 n....
• 9 years agoHelpfull: Yes(2) No(2)
• (x1+x2...+x10)/10=50 and (x12+x13+....+x22)/11=40
  so (550+X11+440)/22=45
  then we get x11=1 ans
• 11 years agoHelpfull: Yes(0) No(9)
• Understand this, 4 raise to 16 is divisible by 3¹, 4 raise to 17 by 3²,
  4 raise to 18 by 3³....our qs is 44⁴⁴
  now 44 raise to 6 is divisible by 3¹, hence 44 raise to 7 will be divisible by 3² and so on.....solving further 44⁴⁴ will be divisible by 3 raise to 39
  
• 11 years agoHelpfull: Yes(0) No(6)
• from options it will be clear 3^n divides 36
• 11 years agoHelpfull: Yes(0) No(0)