Question

The sum of all the elements in the set $\{n \in\{1,2, \ldots \ldots .100\} \mid$ H.C.F. of $n$ and 2040 is 1$\}$ is equal to _______

Answer 1

$2040=2^{3} \times 3 \times 5 \times 17$
$n$ should not be multiple of $2,3,5$ and 17
Sum of all $n=(1+3+5 \ldots \ldots+99)-(3+9+15+$
$21+\ldots \ldots \ldots+99)-(5+25+35+55+65+85+95)-(17) $
$=2500-\frac{17}{2}(3+99)-365-17 $
$=2500-867-365-17$
$=1251$