Describe $\text{Jac}(n\mathbb Z)$ in terms of the prime factorization of $n$ Let $I$ be an ideal of the commutative ring $R$ and define 
$\mathrm{Jac}(I)$ to be the intersection of all maximal ideals of $R$ that contain $I$.

Let  $n > 1$ be an integer. Describe $\text{Jac}(n\mathbb Z)$ in terms of the prime factorization of $n$. (in ring $\mathbb Z$)

I have no idea how to start it.

Hints : 


*

*In $\mathbb Z$, an ideal $I\ne ${$0$} is a prime ideal if and only if it is a maximal ideal, if and only if $I=p\mathbb Z$ for some prime number $p$. 

*An ideal $I=m\mathbb Z$ in $\mathbb Z$ contains $n\mathbb Z$, if and only if $m|n$

*Jac $n\mathbb Z=m\mathbb Z$, where $m$ is the product of the prime factors of $n$.
