The main thing that matters is temperature, habitable zone means water must be able to be in the liquid state.
Temperature depends on the stars radiation and distance. From brightness and size of a star you can calculate how much light it radiates wich then gives a curve of possible temperatures around the star (if you move further away the density of light that hits a potential planet goes down with distance squared)
Especially for very small stars other nasty effects can make the habitable zone smaller, for example very close to the star there can’t be stable planets due to the immense tidal forces of the stars gravity. Our closest star Proxima Centauri for example has no habitable zone as the range of good temperatures is so close to the star that no planet can exist there.
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