Gaining the strength to do traditional push-ups is a progression. In the video below, Shawn shows you an easy and safe way to gradually increase that strength. If you do three sets of 10 push-ups every day at a level that is challenging to you (a level that allows you to use good form but exhausts your muscles by 10-12 repetitions), you will eventually work yourself to the floor. Try it!
Then make a habit of doing three sets a day and keep that strength forever.