The Samsung WB250F has 4.0mm-72.0mm printed on its lens, and its 35mm equivalent focal length range is 24mm-432mm.
Does that mean it has a 6x crop factor?
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Yes, this mean crop-factor of your camera (Samsung WB250F) is 6
Focal length is one of the ways to calculate crop-factor, divide 35 equivalent of focal length to the focal length on the lens
P.S. The canonical way (as far as I know) is to use the size of the sensor and compare it with the size of fullframe sensor. Check here for reference
Yes. Compact cameras label their lenses in "35mm equivalent focal length" which is pretty illogical in my opinion. Thankfully other non-35mm formats such as m4/3 and APS-C and the various medium and large formats do not do the same.
What this means is that your camera with its tiny (roughly 1/2.3" format [though that's not the actual measurement, just a name, consult Wikipedia for more] I believe) sensor and 4-72mm lens has the same field of view that a 35mm sensor and 24-432mm lens would have.