Thank you for reporting, we will resolve it shortly
Q.
If total number of even divisors of 1323000 which are divisible by 105 is $2^k-10$, then $k$ is equal to
Permutations and Combinations
Solution:
$ 1323000=2^3 \cdot 3^3 \cdot 5^3 \cdot 7^2 $
$105=3 \cdot 5 \cdot 7$
$\therefore$ Number of even divisors of 1323000 which are divisible by $105=3 \times 3 \times 3 \times 2=54$
$\therefore 2^{ k }-10=54 \Rightarrow 2^{ k }=64 \Rightarrow k =6$