highest power on 990 which exactly divide 1090!

• 990 = 2*3^2*5*11
  now 1090/2+1090/4+1090/8+1090/16+1090/32+1090/64+1090/128+1090/256+1090/512+1090/1024 = 545+272+136+68+34+17+8+4+2+1=1087
  
  1090/3+1090/9+1090/27+1090/81+1090/243+1090/729 = 363+121+40+13+4+1 = 542
  
  1090/5+1090/25+1090/125+1090/625 = 218+43+8+1 = 270
  
  1090/11+1090/121 = 99+9 = 108
  
  therefore min(1087,542,270,108) = 108 answer
• 10 years agoHelpfull: Yes(4) No(1)
• factors of 990 = 2*3^2*5*11
  so the highest power on 990 which exactly divides 1090! is
  = [1090/11] + [1090/11^2]
  = 99 + 9
  = 108
  
  so the highest power is 108
• 10 years agoHelpfull: Yes(2) No(0)
• 108
  
  990 = 11*10*9
  
  1090! = 1090 * 1089!
  1089! has 11,22,33,... , 121,242,363, ... 1089
  In total, there are 99 + 9 = 108 => 11^108
  
  => Highest power of 990 which divides 10901 = 108
  
  
• 10 years agoHelpfull: Yes(1) No(0)