Let n be a non-negative integer. Then the number of divisors of the...

Let $N = {2}^{10} \times {5}^{10} \times {11}^{11} \times {13}^{13}$

Now, power of $2$ must be zero,

Power of $5$ can be anything,

Power of $13$ can be anything.

But, power of $11$ should be even.

So, required number of divisors is

$1 \times 11 \times 14 \times 6 = 924 .$