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Square factorials

Source: Woody at Maths Jam
Multiply together the first 100 factorials:
$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

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If you enjoyed this puzzle, check out Sunday Afternoon Maths LVII,
puzzles about square numbers, or a random puzzle.
© Matthew Scroggs 2019