Question

If the sum of $1! + 2! + 3! + \cdots + 49! + 50!$ is divided by $15$, what is the remainder?

Answer 1

3

Explanation:

All factorials 5 and above are evenly divisible by 15, so have no remainder. Thus, you are interested in ...

mod(1! +2! +3! +4!, 15) = mod(1 +2 +6 +24, 15)

= mod(33, 15) = 3

The remainder is 3.