Faroe Islands is about 226 times smaller than New Mexico.

New Mexico is approximately 314,310 sq km, while Faroe Islands is approximately 1,393 sq km, making Faroe Islands 0.44% the size of New Mexico. Meanwhile, the population of New Mexico is ~2.1 million people (2.0 million fewer people live in Faroe Islands).
Tip: This to-scale comparison of New Mexico vs. Faroe Islands uses the Mercator projection, which distorts the size of regions near the poles.