Divisible by 1599

Since $( 1700! ) ^ { 2 }$ is much larger than $3400!$ , and using the Sterling's law , we get 1700! = $\displaystyle \sqrt { 2 \times \pi \times 1700 } \left ( \frac { 1700 } { e } \right ) ^ { 1700 } = \sqrt { 3400\pi } \left ( \frac { 1700 ^ { 1700 } } { e ^ { 1700 } } \right )$ , and 3400! = $\displaystyle \sqrt { 6800\pi } \left ( \frac { 3400 ^ { 3400 } } { e ^ { 3400 } } \right )$ .

Then, $\displaystyle \left ( \sqrt { 3400\pi } \left ( \frac { 1700 ^ { 1700 } } { e ^ { 1700 } } \right ) \right ) ^ { 2 } > \sqrt { 6800\pi } \left ( \frac { 3400 ^ { 3400 } } { e ^ { 3400 } } \right )$ .

So, $\displaystyle \frac { 3400! } { \left ( 1700! \right ) ^ { 2 } }$ is not divisible(undivisible) by 1599.