Danny wrote the following product:

\[\large 1! \times 2! \times 3! \times \cdots \times 119! \times 120! \]

He took out one of the following factorials and found that the product had become a perfect square. Find the factorial.

**Notation**: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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