Divisible subdivisions

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