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The concept of common factors does not work with fractions because, once the domain is the rationals rather than integers, any rational can divide into any other rational. So any number can be a common factor and, therefore, there cannot be a greatest one.
For example, consider 1000.
25/1000 = 0.025
1.50/1000 = 0.00150
75/1000 = 0.075
3.00/1000 = 0.00300
Thuse, 1000 can be considered a common factor. But by the same argument, so can 1,000,000; a billion, a googol.
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