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Since 7 is a prime, 7*1 = 7, so that the only possibility for a number to have 7 factors is to have only one prime factor to the power of 6, because 7 = 1 + 6.

64 = 26 = 7 factors (6 + 1) (2 is the smallest Prime number)

Since 36 > 100, then 64 is the only number between 0 and 100 that have 7 factors.

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Q: Which numbers between 0 and 100 have 7 factors?
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