To be clear, lenses don't have a crop factor. Lenses project an image circle of a certain size. When the image circle is smaller than is needed to cover a full camera sensor, you will get dark corners or in some extreme cases, the outline of a circle.
As long as the sensor is smaller than the image circle, though, you will get an image that covers the entire sensor. If the sensor is 24x36mm (full frame), this would be referred to as a "1x" crop factor in modern terminology.
If you put a smaller sensor with the same lens or only capture a portion of the above sensor, the crop factor will increase. We usually calculate this by calculating the diagonal lengths of the sensors and dividing them (or the areas of the sensors and dividing them). So a sensor of around 22.3 x 14.9mm ends up with a diagonal about 1.5x that of 24x36 and Micro 4/3 is about 2x.
If you then choose to use only a portion of the Micro 4/3 sensor, the crop factor would increase again. So in raw, going to 4k from 6k is usually an additional 1.5x crop and going to 2k from 6k will be closer to a 2x crop.