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There is no upper limit. For example, take the powers of 2: 1 has 1 factor (1), 2 has two factors (1, 2), 4 has 3 factors (1, 2, 4), 8 has 4 factors (1, 2, 4, 8), etc.; you can keep multiplying indefinitely by 2, to add one more factor.

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Q: What is the maximum number of factors a number can have?
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