Cocos (Keeling) Islands is about 22,451 times smaller than New Mexico.

New Mexico is approximately 314,310 sq km, while Cocos (Keeling) Islands is approximately 14 sq km, making Cocos (Keeling) Islands 0.0% the size of New Mexico. Meanwhile, the population of New Mexico is ~2.1 million people (2.1 million fewer people live in Cocos (Keeling) Islands).
Tip: This to-scale comparison of New Mexico vs. Cocos (Keeling) Islands uses the Mercator projection, which distorts the size of regions near the poles.