Sum! Divided by 100

Number Theory Level 2

What is the remainder when $1! + 2! + 3! + \ldots + 29! + 30!$ is divided by $100$ ?

Details and assumptions

The notation $n!$ (read as $n$ factorial) refers to multiplying all the positive integers from $1$ to $n$ . For example, $8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ .