Thread: what is the remainder when

1!+2!+3!+4!+.....+100! is devided by 15 ? and how to calculate it ?

Hello,

You can notice that 15=3x5

This means that for all n > (or equal) 5, n! will contain 15 in its factors.

So we know that (5!+6!+...+100!) is a multiple of 15.

1!+2!+3!+4!=1+2+6+24=33

--> the remainder is 3.