9^n is divisible by 144!. then what is the value of n?

• 9 is 3*3=3^2..so,
  144/3=48
  48/3=16
  16/3=5
  5/3=1
  add all qotients=48+16+5+1=70,,,,,70/2(70 divided by 2 because of 3 power 2 )=35
  Answer is 35...
• 10 years agoHelpfull: Yes(27) No(0)
• answer is 35
  process is like how we check number of zeroes in some n!
  now 144!/9^n
  break 9 into least prime
  so now 144/3 + 144/9 + 144/27 + 144/81 ...
  48 + 16 + 5 + 1 we take only integer value
  now total is 70 but we checked for 3 so answer is 70/2 ; power factor of 3 is 2
  so 35
  
• 9 years agoHelpfull: Yes(4) No(0)
• 1 to 100 there are 11 no. Which are divisible by 9 and 100 to 144..... there are total 5 no. So for complete divison total 16 9s are required...
• 10 years agoHelpfull: Yes(3) No(0)
• 144/2=72
  72/2=36
  36/2=18
  18/2=9
  9/2=4
  4/2=2
  2/2=1
  72+36+18+9+4+2+1=142
• 10 years agoHelpfull: Yes(1) No(9)
• wrong question.....144! is divisible by 9^35....9^35 is not divisible by 144!
• 9 years agoHelpfull: Yes(1) No(5)
• as i take ref from keerthi,arkja both the ans are write but some people may not understand how 70 is becoming 35
  that is very simple 70 is for no of 3's in 144! but in question they asked no of 9's so half the no of 70 which is 35
• 7 years agoHelpfull: Yes(1) No(0)
• Will ti possible? coz when we look for any power of 9 it will end with unit digit either 9 or 1 and 144! ends with unit digit 0
• 10 years agoHelpfull: Yes(0) No(9)
• I think answer is 35 !
• 10 years agoHelpfull: Yes(0) No(1)