Question

Total number of even divisors of $189000$ that are divisible by $15$ are $\lambda$, then $\frac{\lambda }{9}$ is equal to

• A. $2$
• B. $3$
• C. $5$
• D. $6$

Answer 1

Answer: (D)

$6$

$189000=2^3{.3}^3{.5}^3.7$
For the divisors to be even and divisible by $15$
$2,3$ and $5$ must occur at least once.
Therefore total number of required divisors are :

$\lambda =3\times 3\times 3\times 2=54$

Thus, $\frac{\lambda }{9}=6$