Question

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

Answer 1

Answer: 1251

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