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Get in the habit of rinsing your razor blades after each use. This will keep skin and hair particles, soap scum and other debris from building up in the first place.   Consistent cleaning will go a long way in extending a razor’s lifespan, even if it’s of the disposable variety. Once a week or so, disinfect your razor by soaking it in rubbing alcohol. The best way to store loose razor blades is in an enclosed case or similar container that shuts securely. If you use the razor to shave, you can rest it on a separate base or stand or position it upright in a cup to allow water to drain out of it. Keep the blade ventilated until it's dry, then put it away where it won't become damaged or cause an accident.  Don’t leave your razor sitting on the edge of the sink or on the alcove in a dingy shower, where they’ll be in direct contact with soap scum and bacteria. These places also tend to be more humid, which increases the likelihood of rusty blades.
Clean the razor regularly. Keep your razor in a clean, dry environment.