Trim It To A Nub
Keep your hangnail trimmed so it’s as close to the skin as possible. The more of a nub it is, the less nail that’ll stick out and the less likely it’ll get snagged on your shirt or pants. That’ll require a quality pair of nail clippers. Try the Seki Edge Stainless Steel Fingernail Clipper ($13 @ Amazon.com)
Also: How To Stop Biting Your Nails
Keep It Covered
If your trim job (heh heh) didn’t snip away enough and you’re concerned of a snag, keep it covered. Instead of a band-aid, which can become a bacteria trap, use a liquid bandage like New Skin ($6 @ Amazon.com).
Soften Your Cuticles
A softened hang nail will be less likely to snag against clothing or rip off. Doubling up on a trim and some softener doubles your chances of not having any nail nub snaggage. Soak your hand in warm water in the a.m. before you take off for work.
Another option is to buy a cuticle softener, like Super Nail Cuticle Softener ($6.50 @ Amazon.com). Rub a glob on and it’ll moisturize your cuticles as it softenes. That’s called a win-win.