what is the remainder when 4.4!*5.5!*6.6!...........19*19! is divided by 64

• i) if the question is 4.4!*5.5!*6.6!...........19*19! then answer is zero
  ii) if the question is 4*4! + 5*5! + 6*6! +...................+ 19*19! answer is 3.
  in second case : from from 8*8!, it will be divisible.(bcaz futhur in 9!, there will be 8*4*2 ) and from 4*4! to 7*7!
  
  if u take common 24 i.e 4! , 24(4+25+30+1470)/64, 3(1529)/8 , remainder will be 3.
  
  
  
  
• 8 years agoHelpfull: Yes(15) No(5)
• 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!/64)-(4!/64)
  
  (20!/64)=r(0)
  (4!/64)=r(3)
  
  
  anzs 3
  
• 8 years agoHelpfull: Yes(14) No(15)
• I think Zero(0)
  because (4*4*3*2*5*5!*6*5*.......*1*7*7!..........)/64=(int value) no remender there
• 8 years agoHelpfull: Yes(10) No(7)
• All the above terms greater than or equal to 8.8! , they will be completely divisible by 64.
  
  Now the question becomes : 4.4! + 5.5! + 6.6! + 7.7!
  
  dividing each of the four term seperately, the remainders will be 32 , 24 , 32 , 16
  
  So adding these remainders together will make 106 and again dividing them by 64 will gives the final remainder as : 40
• 7 years agoHelpfull: Yes(9) No(1)
• The remainder would be 40
  as the final result will be (20!-4!)/64 = 20!/64 - 4!/64
  20!/64 = 0
  -4!/64 = -24/64
  which gives -24 as remainder which means real answer would be -24+64= 40
• 7 years agoHelpfull: Yes(9) No(0)
• Actual question is
  4*4! + 5*5! + 6*6! +...................+ 19*19! is dividede by 64.
  Find the remainder.
  1) 3
  2) 3√3
  3) 9/2
  4) don't remember
• 8 years agoHelpfull: Yes(5) No(4)
• 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!/64)-(4!/64)
  
  (20!/64)=r(0)
  (4!/64)=r(4)
  
  therefore combined the remainder is 60(-4)
  
• 8 years agoHelpfull: Yes(4) No(0)
• 40 is the ans
  since 20!/64 rem is 0
  4!/64 we get 24 rem
  so 20!/64-2!/64 gives rem as 0-24/64=-24/64=40/64 so 40 is the rem
• 7 years agoHelpfull: Yes(2) No(0)
• zero..... cz its a multiplication chain and one can easily spot a 8*8 in the series!!
• 8 years agoHelpfull: Yes(1) No(1)
• From 8! Containing 8*7*6*5*4*3*2 =64*7*6*5*3
  From 8 onwards totally divisible by 64 leaving remainder as zero
  Before 8! Total value = 40296/64 = 40 remainder
• 7 years agoHelpfull: Yes(1) No(0)
• 56 is the answer.As after 7! every number is divisible by 64,,,add upto 7! and divide hat by 64 to get remainder
• 8 years agoHelpfull: Yes(0) No(1)
• ans is 20;for dividng by 64 ,we want 2 power 6,which is possible after 8*8!.so upto 4*4!+5*5!+6*6!+7*7!which when divide by 64 gives remainder 20.check .i have done it.if any mistake correct me.
  
• 8 years agoHelpfull: Yes(0) No(1)
• Bt the option r different
• 8 years agoHelpfull: Yes(0) No(0)