The "Perfect Pushup"
It is a misconception that a pushup only works your upper body. The “perfect pushup” is actually a total body movement.
Your triceps, chest, and biceps are the key muscles in the pushup, but your abs, hips, and legs help stabilize your core during and after the repetition.
When doing a pushup, a wide or narrow grip is ok. A narrow grip will isolate the triceps a bit more than the chest, and the wide grip will isolate the muscles of your chest more through the repetition.
A piece of the body that is overlooked during a pushup is the upper back, you want to make sure it is active during the release as well as the contraction. Your shoulder blades should squeeze together on the way down. The more of your muscles working together the less fatigue you should feel in the first few reps, the more reps you do the more fatigue you will feel. That is why you should work on the quality of your pushups not the quantity.
The better and more efficient you become with your pushups the more you will ultimately be able to conquer at a time.