# (1!+2!+3!+......100!)/100.= ...... Find the remainder ?

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HSBC244 Share
Sep 21, 2017

Remainder is $13$

#### Explanation:

We know that

1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3,628,800

From here on in, the numbers will always end with at least two zeroes, so we know the last two numbers won't change.

The sum of the first $10$ factorials ends with a $13$, which will be the remainder.

Hopefully this helps!

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