what is the reminder when 4.4!+5.5!+6.6!+7.7!+..............+19.19! is divided by 64.

• E = 4*4! + 5*5! + 6*6! ........19*19!
  E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
  E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
  E = (20!-4!)
  
  E/64 = (20!-4!)/64
  => rem = 0-24/64 = -24/64
  => rem = -24+64 = 40
  
• 10 years agoHelpfull: Yes(92) No(2)
• 4*4! + 5*5! + 6*6! ........19*19!
  (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
  (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
  (20!-4!)
  
  (20!-4!)/64
  20!=20*19*18...16...*4*...1
  as 16*4=64....the rem we get as 0
  so dividing 20!/64=0(as rem is 0)
  rem=0-4!/64=-24/64=64-24=40
  hence ans is 40
  
• 10 years agoHelpfull: Yes(25) No(0)
• can anyone explain how
  (20!-4!)/64
  =0-24/64
  ???
• 10 years agoHelpfull: Yes(16) No(1)
• 40..8.8! is divisible by 64..we have to calculate 4.4!+5.5!+6.6!+7.7!/64 that is =40
• 10 years agoHelpfull: Yes(9) No(1)
• 40
  (5-1)4!+..........(20-1)5!
  (5!-4!+6!-5!........20!-19!)/64
  (20!-4!)/64
  (0-4!)/64
  -24/64
  64-24=40
• 10 years agoHelpfull: Yes(6) No(0)
• 40
• 10 years agoHelpfull: Yes(1) No(0)
• what is the formula to calculate the sum of factorial of n natural number?
• 10 years agoHelpfull: Yes(0) No(0)
• 4*4!=4 *24=96
  5*5!=120*5=600 and all else numbers products ends with 00 so if we add we get 96 in tens and units place so 96%64 is the answer
• 10 years agoHelpfull: Yes(0) No(0)
• the remainder will be 2+2=4
  
• 10 years agoHelpfull: Yes(0) No(1)
• Remainder of [ (4.4!+5.5!)/64 + (6.6!+7.7!+...........+19.19!)/64]
  = Remaider of [(96+600)/64)] + Remainder of [( 6.6!+7.7!+...........+19.19!)/64)]
  = 56 + 0
  = 56
• 9 years agoHelpfull: Yes(0) No(1)