Coupling factor:

If all the flux of a primary coil links with all the turns of a secondary then 100% coupling exists. Sometimes it is more convenient to use a coupling factor - k.
Maximum Coupling (100%) is represented by a k value of 1.
Thus if flux linkage is 97% the coupling factor is 0.97.
Given that mutual coupling depends on k then so does the mutual inductance. The relationship is given by: M = k√ (L₁ L₂ )
Where L1 and L2 are individual inductance's of the mutually coupled coils.
The value of k depends on:
• Purpose of coils involved
• Relative positions of the coils
• Frequency or rate of change of current
and can be as high as 0.98 or as low as 0.0001.