Compute the fixed divisor of $a\left(x\right)$ in $Z_x$.  The fixed divisor is the largest integer that divides $a\left(k\right)$ for all k in $Z$.  For primitive polynomials, the fixed divisor is no greater than $n!$ where $n=\mathrm{degree}\left(a\,x\right)$.

The probability that the fixed divisor is greater than one for random polynomials of degree n is approximately 0.278 as n goes to infinity.

$\mathrm{fixdiv}\left(x\left(x+1\right)\left(x+2\right)\left(x+3\right)\,x\right)$

$24$