FIND THE REMAINDER

just add 1!+2!+3! =9 because other numbers will be divisible by 24 so the answer is $\boxed{9}$

Notice that $4!=24$

Then clearly, $4! \equiv 0 (mod 24)$

Therefore for any n! where n is greater than 4, n! will have 24 as a factor and therefore leave no remainder when divided by 24.

It follows that $4!+5!+6!+...+100!\equiv 0(mod24)$

And then all that is left over is $1!+2!+3!=9$

The remainder, therefore, is $\boxed { 9 }$