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(Abridged) Context: The assumption of a gas-to-dust mass ratio (\gamma) is acommon approach to estimate the basic properties of molecular clouds, such astotal mass and column density of molecular hydrogen, from (sub)mm continuumobservations of the dust. In the Milky Way a single value is used at allgalactocentric radii, independently of the observed metallicity gradients. Bothmodels and extragalactic observations suggest that this quantity increases fordecreasing metallicity Z, typical of the outer regions in disks, where fewerheavy elements are available to form dust grains.  Aims: We aim to investigate the variation of the gas-to-dust ratio as afunction of galactocentric radius and metallicity, to allow a more accuratecharacterisation of the quantity of molecular gas across the galactic disk, asderived from observations of the dust.  Methods: Observations of the optically thin C\$^{18}\$O (2-1) transition wereobtained with the APEX telescope for a sample of 23 massive and densestar-forming regions in the far outer Galaxy (galactocentric distance greaterthan 14 kpc). From the modelling of this line and of the spectral energydistribution of the selected clumps we computed the gas-to-dust ratio andcompared it to that of well-studied sources from the ATLASGAL TOP100 sample inthe inner galactic disk.  Results: The gradient in gas-to-dust ratio is found to be 0.087 dex/kpc (orequivalently \gamma\ proportional to Z\$^{-1.4}\$). The dust-to-metal ratio,decreases with galactocentric radius, which is the most common situation alsofor external late-type galaxies. This suggests that grain growth dominates overdestruction. The predicted gas-to-dust ratio is in excellent agreement with theestimates in Magellanic clouds, for the appropriate value of Z.

Galactocentric variation of the gas-to-dust ratio and its relation with metallicity