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

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- May 8th 2008, 03:26 AMgiggliewhat is the remainder when
1!+2!+3!+4!+.....+100! is devided by 15 ? and how to calculate it ?

- May 8th 2008, 03:31 AMMoo
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.