(1!+2!+3!.........+50!)is divided by 5 then what wil b the remainder

• (1!+2!+3!.........+50!)is divided by 5 then what wil b the remainder
  
  The remainder will be same as (1!+2!+3!+4!)is divided by 5 .
  (1!+2!+3!+4!)=1+2+6+24=33
  when 33 is divided by 5, remainder is 3.
  So when (1!+2!+3!.........+50!)is divided by 5 then remainder is 3.
• 12 years agoHelpfull: Yes(22) No(7)
• always take the sum till the even term since 50th term is naturally even, i.e. 1!+2! or 1!+2!+3!+4! likewise..
  so if we take, 1!+2!+3!+4! = 33
  now, 33/5 leaves a remainder 3.
  Hence, 3 is the desired ans.
  
• 12 years agoHelpfull: Yes(13) No(1)
• We just need to find which smallest factorial’s value is 5 or is a multiple of 5. Because any multiple of 5 divided by 5 leaves a remainder of zero.
  We know that value of 5! is 120. If 5! = 120, it is guaranteed that all the factorials ahead of it will be a multiple of 5 as n! = n × (n – 1)! .
  So, all the factorials starting from 5! onwards when divided by 5 will leave a remainder of zero. So. Our answer is dependent on the first 4 terms.
  So, when (1! + 2! + 3! + 4!) ÷ 5=(1+2+6+24)/5 the remainder is 3.
• 12 years agoHelpfull: Yes(10) No(0)
• soln not clear...any other way?
• 12 years agoHelpfull: Yes(1) No(1)
• 153 will be the remainder and 153/5=3 as remander 1 to 5 factorial will be the possible remainder rest all will be divisible by 5
  any other questions or doubts u have pls mail me to shyamleshd@gmail.com
• 12 years agoHelpfull: Yes(1) No(3)
• 
  The remainder will be same as (1!+2!+3!+4!)is divided by 5 .
  
  WHY SO ?????????????????
• 12 years agoHelpfull: Yes(1) No(1)
• not clear can u explain in a clear way?
• 12 years agoHelpfull: Yes(0) No(1)