This is a simple question with a rather complex answer. Successful flea control has two aspects. Fleas must be controlled on your cat, and fleas must be controlled in your cat's environment. Since cats and dogs share the same fleas, the presence of a dog in your cat's environment makes flea control much more difficult. To appreciate the complex issue of flea control, you must understand something about the flea's life cycle.
Fleas seem to be rather simple creatures.
Although you are only able to see the adult flea, there are actually four stages of the life cycle. They are too small to see without magnification. Fleas lay their eggs on the cat, but the eggs do not stick to the cat's hair. Instead, they fall off into the cat's environment. They hatch into larvae in 1 to 10 days, depending on temperature and humidity.