Mathematics - Permutation & Combination Question with Solution | TestHub

Prime factorisation of $36=2\times 2\times 3\times 3$

So, for number having G.C.D with $36$ to be $2$, the number should be odd multiple of $2$ and does not have factor $3$ and $9$

$\Rightarrow$Odd multiple of $2$ are

$\left\{102,106,110,114\dots \dots .998\right\} \left(225 \text{numbers}\right)$

$\Rightarrow$No. of multiples of $3$ are

$\left\{102,114,126\dots \dots .990\right\} \left(75 \text{numbers}\right)$

Which also include multiple of $9$

Hence, Required $=225-75=150$