Chocolates Distribution

Question

$ A\ man \ has \ 1!+2!+3!+...... +1000! \ chocolates \ which \ he \ has \ to \ divide \ equally \ among \ \color{red} n  \ children.

\ Least \ possible  \ value \  of  \ \color{red}n  \ is $

Comments

least possible value of n could be 1, but least possible value of n>1 will be,

1! + 2! + 3! +4! + 5! + 6!......1000!  =  1 + 2 + 2.3 + 2.3.4 + 2.3.4.5 + 2.3.4.5.6.........

=3 + 2.3 + 2.3.4 + 2.3.4.5 + 2.3.4.5.6.......

taking 3 common out -> 3(1 + 2 + 2.4 + 2.4.5 + 2.4.5.6..........), now since 3 is a factor of above series therefore n=3 will be minimum value such that chcolates are distributed equally.

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In some ,question modified by removing that least part ..

Is 5,7 possible?