The Legality of a Fake Social Security Number Request

Suzanne in Kansas says, my daughter attends college two and a half hours away from our home. She'll be a junior in the fall and apply for space in an apartment with two other roommates. The online application is the only way to apply and there's a mandatory section requiring her social security number. Is this legal, why do they want this information? I can't find those fake social security numbers you suggested on your website, where are they? And could she be denied her apartment if it comes up as a fake number?