Question

Number of divisors of $2^5{3}^2{.5}^3$ which are divisible by $2$ but not divisible by $6$ and $8,$ is

• A. $8$
• B. $12$
• C. $20$
• D. $72$

Answer 1

The correct option is A $8$

$2^5{3}^2{5}^3$

The numbers can be form of $2^x{3}^y{5}^z$

but since it is not divisible by $6,8$

So, it shall contain more power of $42$ of 2.

Must not contain $2$ and $3$ together so if $2$ is there then choices are:

$(2^1{5}^1,2^2{5}^2,2^2{5}^3,2^1{5}^2,2^1{5}^3,2^1{5}^0,2^2{5}^0,2^2{5}^1)$

and without $2.$ It is not possible as it must be divisible by $2$.

So, $8.$

Hence, the answer is $8.$