There are several home remedies that you can try to keep your cat’s coat healthy and clean:

1. Brush your cat regularly: Brushing helps to remove dirt, tangles, and loose fur from your cat’s coat, which can help to keep it clean and healthy. It also helps to stimulate the skin and promote circulation.
2. Bathe your cat: If your cat gets particularly dirty or has a strong odor, you can give them a bath. Use a mild cat shampoo and make sure to rinse thoroughly to avoid leaving any soap residue on their skin.
3. Try a coconut oil treatment: Coconut oil can help to moisturize your cat’s skin and coat, and may help to reduce shedding. Simply rub a small amount of coconut oil into your cat’s coat, avoiding the face, and then brush it through.
4. Use a de-shedding tool: If your cat has a thick or long coat, a de-shedding tool can help to remove excess fur, which can help to keep their coat clean and healthy.
5. Feed your cat a healthy diet: A healthy diet is important for maintaining a healthy coat in cats. Make sure your cat is getting all the nutrients they need, including protein, fatty acids, and vitamins.
6. Avoid using harsh chemicals: Harsh chemicals, such as those found in some shampoos and flea treatments, can be irritating to your cat’s skin and may strip their coat of natural oils. Instead, look for natural or organic products.