Faroe Islands is about 1,063 times smaller than Alaska.

Alaska is approximately 1,481,348 sq km, while Faroe Islands is approximately 1,393 sq km, making Faroe Islands 0.09% the size of Alaska. Meanwhile, the population of Alaska is ~710,231 people (657,962 fewer people live in Faroe Islands).
Tip: This to-scale comparison of Alaska vs. Faroe Islands uses the Mercator projection, which distorts the size of regions near the poles.