You may find this previoius discussion on the old BB answers your query, but in summary although we call it a "fusing" factor, it is really just a de-rating to handle the fact that neither fuses nor breakers have an instant transition from tripping to not tripping at the rated current.
Rather there is a soft transition between some lower limit value of 'never trip' and a higher limit current of 'always trip' with a fair amount of uncertainty about what will happen and how fast, for any current of intermediate value.
So a 13A fuse will carry 13A all day at room temperarture without operating, (the never trip condition) and will fire in a some seconds to minutes at 20A (the always trip condition) but at anything over 13A but less than 20A may trip or may not, depending on local factors, and the manufactureing tolerances on the fuse wire, the duration of the overload and so on. The fusing factor is just a measure of the ratio of the two limits. A very similar consideration applies to breakers with a thermal mechanism, though the exact factor may vary a bit.
You may find this previoius discussion on the old BB answers your query, but in summary although we call it a "fusing" factor, it is really just a de-rating to handle the fact that neither fuses nor breakers have an instant transition from tripping to not tripping at the rated current.
Rather there is a soft transition between some lower limit value of 'never trip' and a higher limit current of 'always trip' with a fair amount of uncertainty about what will happen and how fast, for any current of intermediate value.
So a 13A fuse will carry 13A all day at room temperarture without operating, (the never trip condition) and will fire in a some seconds to minutes at 20A (the always trip condition) but at anything over 13A but less than 20A may trip or may not, depending on local factors, and the manufactureing tolerances on the fuse wire, the duration of the overload and so on. The fusing factor is just a measure of the ratio of the two limits. A very similar consideration applies to breakers with a thermal mechanism, though the exact factor may vary a bit.