Big Numbers Make Me Cry

What is the remainder when \(2028!\) is divided by \(2029\)?

Details and assumptions

The factorial of a positive integer \(n\), denoted by \(n!\), is the product of all positive inegers less than or equal to \(n\). For example, \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).

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