Question

Let $n$ be a non-negative integer. Then the number of divisors of the form $4n+1$ of the number $(10{)}^{10}\cdot (11{)}^{11}\cdot (13{)}^{13}$ is equal to

Answer 1

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


Number of required divisors $=1\times 11\times 6\times 14$
$=924$