You can hide products with out of stock from the list of products in your store in case you want to hide them from your customers by going to the control panel of your store and follow the following steps:

1-Open Admin panel of Magento store and navigate to System – > Configuration – > Catalog– > Inventory – > Stock Options Section.

2-Set Display Out of Stock product to No:

3-Click Save Config button to apply changes.

*Clear Magento cache to check the changes applied.

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