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An infinite number of numbers have at least 28 factors.

Do you mean what number has exactly 28 factors?

Do you mean exactly 28 prime factors?

The smallest number with 28 prime factors is (2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97 x 101 x 103 x 107), which is approximately 2.5*1042.

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Q: What number has 28 factors?
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