Question:
The total number of 4-digit numbers whose greatest common divisor with 18 is 3 , is
Solution:
Let $N$ be the four digit number $\operatorname{gcd}(N, 18)=3$
Hence $\mathrm{N}$ is an odd integer which is divisible by 3 but not by 9 .
4 digit odd multiples of 3
$1005,1011, \ldots \ldots, 9999 \rightarrow 1500$
4 digit odd multiples of 9
$1017,1035, \ldots \ldots, 9999 \rightarrow 500$
Hence number of such $\mathrm{N}=1000$
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