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32 is the most number of factors for any number less than 1000.

The number is 840

Factors for 840 are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840

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Q: Which numbers under 1000 have the most factors?
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