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There is no such number. You can always find a number that has yet more factors. For example, 4 has three factors (1, 2, 4), 8 has four factors (1, 2, 4, 8), 16 has five factors (1, 2, 4, 8, 16), etc. - and you can continue obtaining higher and higher powers of two, thus obtaining numbers with more factors than the previous one.

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