Neutron stars are formed when large stars run out of fuel and collapse. To get a neutron star, you need to have star that's larger than about 1.5 solar masses and less than 5 times the mass of the Sun.
If you have less than 1.5 solar masses, you don't have enough material and gravity to compress the object down enough. You only get a white dwarf. This is what will happen to our own Sun one day.
If you have more than 5 times the mass of the Sun, your star will end up as a black hole.
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