system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why 1080p and 720p are the standards for HD, why not 750 and 1000?
gpt
Most answers on this thread are either incorrect or just partial answers. 

No, it's not simply because CS uses powers of two. 

There are historical reasons: 

Back in the day, analogue television had limited bandwidth. They used that bandwidth as well as they could and came up with a standard to transmit luminace and chrominance plus audio in that limited bandwidth. Later, when color TV was invented, they had to retrofit more chrominance information into the same bandwidth. The number of lines per second they had to transmit was also constrained by further historical reasons: electricity frequency, which goes back all the way to Tesla, the beginnings of AC, and electric motors. So, NTSC (used in the US) settled for using their 6mhz of bandwidth to transmit a 720x480 image at 29.97FPS. Other standards, PAL and SECAM, for instance, used a higher resolution at a lower framerate (720x576 @25FPS). Again, this was constrained by the fact the US uses 60hz AC, while PAL/SECAM countries (Europe, South America) used 50hz. This where interlaced signals (each frame is actually split in two and transmitted odd / even), that's why framerate is half the electricity frequency. 

With the advent of digital, this same resolutions where used as a starting point. VGA was based on NTSC (640x480). As LCD screens became the norm, progressive video replaced interlaced, and 480p became the standard. Since video needs to keep its aspect ratio, both width and heigh will grow proportionally. 

So, 720p is simply 1.5 times 480p, and 1080p is simply 1.5  times 720. 

480 * 1.5 = 720
720 * 1.5 = 1080

EDIT: 

TL;DR: HD is one and a half times more vertical resolution than standard TV, and Full HD is one and a half times more vertical resolution than HD.