Question

The total number of $3$-digit numbers, whose greatest common divisor with $36$ is $2$, is____.

Answer 1

Answer: 150

$36=2\times 2\times 3\times 3$
Number should be odd multiple of $2$ and does not having factor $3$ and $9$
Odd multiple of $2$ are
$102,106,110,114\dots \dots 998\text{ (225 no.) }$
No. of multiples of $3$ are
$102,114,126\dots \dots 990\text{ (75 no.) }$
Which are also included multiple of 9
Hence,
Required $=225-75=150$