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All factors are whole numbers and all whole numbers are rational numbers (a rational number is one which can be expressed as one integer over another integer, and whole numbers can be expressed as themselves over 1), thus all factors are rational numbers and so all greatest common factors are rational numbers.

The set of whole numbers is a [proper] subset of the set of rational numbers: ℤ ⊂ ℚ

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Q: Can a greatest common factor be a rational number?
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