what will be the remainder if 1!+2!+3!+..+100! is divided by 7

• 7! onwards all terms are divisible by 7 as 7 is one of the factor. So there is no remainder left for those terms i.e. remainder left after dividing 7! + 8! + 9! + ... +100! is 0.
  The only part to be consider is
  = 1! + 2! + 3! + 4! + 5! + 6!
  = 1 + 2 + 6 + 24 + 120 + 720
  = 873
  The remainder left after dividing 873 by 7 is 5
  Hence, the remainder is 5.
• 11 years agoHelpfull: Yes(72) No(0)
• 7! onward terms are divisible by 7...
  Summation till 6!=873
  hence remainder = 873%7 = 5
• 11 years agoHelpfull: Yes(9) No(4)
• all terms from 7 will have the factor 7...so we consider the 1st 6 terms: 1+2+6+24+120+720 thats 873
  which leaves remainder 5 when divided by 7
• 11 years agoHelpfull: Yes(3) No(0)
• after 6! all terms divisible by 7.so we hve to cnsdr 1! +2!+3!+4!+5!+6!=873%7=5
• 11 years agoHelpfull: Yes(2) No(0)
• (1!+3!)+(2!+4!)+(5!+6!)+(7!+8!+9!+..........+100!)
  =(7)+(26)+5!(1+6)+7!(1+8+8.9+............+8.9.10......100)...WE FIND THAT EXCEPT 26 THE SECOND TERM, ALL THE OTHER TERMS ARE DIVISIBLE BY 7.HENCE THE REMAINDER WE GET ON DIVIDING WITH 7 IS THE REMAINDER WE GET WHEN WE DO 26/7...THAT IS ...5 IS THE REMAINDER .
• 11 years agoHelpfull: Yes(1) No(2)
• rearranging the series we get.
  (1!+3!)+(2!+4!)+(5!+6!)+(7!+8!+9!+..........+100!)
  =(7)+(26)+5!(1+6)+7!(1+8+8.9+............+8.9.10......100)...WE FIND THAT EXCEPT 26 THE SECOND TERM, ALL THE OTHER TERMS ARE DIVISIBLE BY 7.HENCE THE REMAINDER WE GET ON DIVIDING WITH 7 IS THE REMAINDER WE GET WHEN WE DO 26/7...THAT IS ...5 IS THE REMAINDER .
• 11 years agoHelpfull: Yes(1) No(0)
• after 7! we don't need to calculate as remainder is 0.
  720+120+24+6+2+1/7=5 as remainder...
• 11 years agoHelpfull: Yes(1) No(0)
• 1+2+6+24+120+720 ;;
  873/7 =>
  remainder: 5
  
• 11 years agoHelpfull: Yes(0) No(0)
• remainder will be 5.
• 11 years agoHelpfull: Yes(0) No(0)