  We prove that for every graph $H$ of maximum degree at most $3$ and for every
positive integer $q$ there is a finite $f=f(H,q)$ such that every $K_f$-minor
contains a subdivision of $H$ in which every edge is replaced by a path whose
length is divisible by $q$. For the case of cycles we show that for $f=O(q \log
q)$ every $K_f$-minor contains a cycle of length divisible by $q$, and observe
that this settles a recent problem of Friedman and the second author about
cycles in (weakly) expanding graphs.
