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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.
If you enjoyed this puzzle, check out Sunday Afternoon Maths LIX,
puzzles about remainders, or a random puzzle.