# 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, $$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$$.

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