The maximum number of divisors of numbers in the int range is 1536

\qquad Given number n,$n<=2^{31}-1$, There is a set of numbers , Its approximate number is 1536, yes int The case with the most divisors in the range .
$1745944200=2^3\ast 3^3\ast 5^2\ast 7\ast 11\ast 13\ast 17\ast 19$
$2113511400=2^3\ast 3^3\ast 5^2\ast 7\ast 11\ast 13\ast 17\ast 23$
\qquad To calculate the number of divisors, you can count first n Do prime factor decomposition , It's written in $n=a_1^{p_1}\ast a_2^{p_2}\ast \cdots \ast a_n^{p_n}$ In the form of , be $n$ The approximate number of is $(p_1+1)\ast (p_2+1)\ast \cdots \ast (p_n+1)$. for example ,1745944200 The approximate number of is $(3+1)\ast (3+1)\ast (2+1)\ast 2\ast 2\ast 2\ast 2\ast 2=1536$