Applied Mechanics and Graphic Statics
The characteristic of a couple is:

A couple can be never the balanced by a single force
All listed here
Algebraic sum of moments of forces, constituting a couple, about any point, is same
Algebraic sum of forces, constituting a couple is zero

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Applied Mechanics and Graphic Statics
If a set of given forces are such that their free vectors build a closed polygon, then

The resultant force is zero but resultant couple is not zero
The resultant force is zero but resultant couple may not be zero
The resultant force and resultant couple are always zero
The resultant force and resultant couple both may not be zero

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