The 80 and 120 are just incidental not chosen, you need to start from the beginning
In the beginning there was NTSC (sorry PAL, you don’t matter here). NTSC was the transmission standard for color TV and gave you an image that was 640 pixels wide and 480 tall (4:3 ratio). The original selection of how many rows/columns is arbitrary, a number had to be chosen and it was chosen to be even and would impact everything to come after.
Then we wished to move to “HD” and handle both standard TV(4:3) and movie formats (21:9) better so they settled on 16:9 ratio. The first was 854:480 but they eventually settled on twice as wide as normal giving you 1280 wide (640×2) and 720 tall. This ensured that normal TV programs still fit, they were just scaled up by 1.5 with black bars on the side, and wide screen movies could show as wide screen with small black bars at the top and bottom.
Full HD boosted the count by 50% in each direction so you ended up with 1920 (640×3) by 1080 giving a bit over 2x the pixel count in total
Then Quad HD comes along and just doubles everything for 4x the pixel count so you get 3840 (640×6) x 2160
Every weird multiplier you find is actually derived from the arbitrary numbers chosen for NTSC back in the 1950s
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