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  4. The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is .

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Q. The total number of $4$-digit numbers whose greatest common divisor with $54$ is $2$, is _____.

JEE MainJEE Main 2023Permutations and Combinations

Solution:

$N$ should be divisible by 2 but not by 3
$N =$ (Numbers divisible by 2 ) $-$ (Numbers divisible by 6$)$
$N =\frac{9000}{2}-\frac{9000}{6}=4500-1500=3000$