There are multiple styles of faucets and replacing the cartridge can vary from style to style. Below are a few examples of replacing the cartridges of the different faucet styles.
Always turn off water before proceeding with replacing the cartridge in your faucet.
Single Lever Handle (top) Faucet
Removing the Handle
Remove the set screw plug (1).
With the valves in "closed" position, unscrew the set screw (2) and remove the handle (3) from the valve stem (4).
Loosen the screw (7) from the valve stem (4).
Loosen the cap (5) from the sleeve (6).
Replacing the Cartridge
Loosen sleeve (1) by turning it counter-clockwise and lift out the cartridge (2).
Remove the old cartridge and replace with the new cartridge.
Replace the sleeve and tighten.
Reinstall the handle.
Single Lever Handle (side) Faucet
Removing the Handle
Unscrew the set screw (1) on the handle (2).
Remove the handle (2) and unscrew the screw (3).
Remove the cap (4).
Replacing the Cartridge
Loosen the cartridge nut (1) by turning it counter-clockwise and lift out the cartridge (2).
Insert the new cartridge.
Reinstall the handle.
Two Lever Handle Bridge Faucet
Raising the Body
Loosen the screws (2) and raise the faucet (1).
Turn the tubes (3) clockwise.
Replacing the Cartridge
Loosen the cartridge nuts (1) and remove the old cartridges (2).
Replace with the new cartridges.
Replace the cartridge nuts (1) and tighten.
Replacing the Body
Turn the tubes (3) counterclockwise and reinstall the faucet (1).
