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If p is any Prime number, then p12 would meet the requirements. The seven factor pairs would be:

(p0, p12)

(p1, p11)

(p2, p10)

(p3, p9)

(p4, p8)

(p5, p7)

(p6, p6)

It can be shown that, because 7 is a prime, a composite number cannot generate such a solution.

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Q: What number has exactly 7 factor pairs?
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