S=1,,2022.

Question

$S=\{1,\dots,2022\}$. Find the probability that a randomly chosen $n\in S$ satisfies $\gcd(n,2022)=1$.

Accepted Answer

$2022=2\times3\times337$. By inclusion-exclusion, numbers divisible by 2, 3 or 337: $1011+674+6-337-3-2+1=1350$ (computed via the standard sieve, matching the source's total $1350$).

$$P = \frac{2022-1350}{2022}=\frac{672}{2022}=\frac{112}{337}$$

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