For $1024 \times 768$ I can see that $768/1024 = 0.75$, i.e. $\frac34$, so $4:3$ makes sense. How do I do it for other resolutions like $1920 \times 1080$ though?
2026-03-29 15:54:35.1774799675
How do I work out the aspect ratio from the resolution by hand?
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All you have to do is divide out the common factors until the two terms are coprime (unless they're the same to begin with, e.g., a square image). With your second example, I'd first divide out the 10, giving me 192:108, then I'd divide by 2, going to 96:54, and 48:27; then clearly you divide out the 3s, leading to 16:9.
I take it step-by-step like that because you said "by hand." With a computer, I'd just have it tell me $\gcd(1920, 1080)$, or better yet, have it express $\frac{1920}{1080}$ in lowest terms for me.