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A number with exactly five factors is a number that is a prime number raised to the fourth power (p4). The factors are 1, p, p2, p3, and p4.

Examples:

The 5 factors of 24 = 16 are 1, 2, 4, 8, and 16.

The 5 factors of 34 = 81 are 1, 3, 9, 27, and 81.

The 5 factors of 54 = 625 are 1, 5, 25, 125, and 625.

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Q: What numbers have exactly five factors?
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How many square numbers are between 1 and 1000 that have five factors?

There are three of them with exactly five factors.


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