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No. The same quantities in different units.
It can be a conversion factor - though not necessarily. For example, 68 deg Fahrenheit = 20 deg Celsius. But there is no conversion factor for F-to-C: instead there is a linear equation.
Use a conversion factor
You use a conversion factor when you want to convert something to something else - for example, to convert between different units of measurement.
It is the units for the measurement which you are converting FROM.