We present an aerosol cloud condensation nuclei (CCN) closure study over the north-east Atlantic Ocean using six approximating methods. The CCN number concentrations (N.sub.CCN) were measured at four discrete supersaturations (SSs; 0.25 %, 0.5 %, 0.75 % and 1.0 %). Concurrently, aerosol number size distribution, sub-saturation hygroscopic growth factor and bulk PM.sub.1 chemical composition were obtained at matching time resolution and after a careful data validation exercise. Method A used a constant bulk hygroscopicity parameter Îº of 0.3; method B used bulk PM.sub.1 chemical composition measured by an aerosol mass spectrometer (AMS); method C utilised a single growth factor (GF) size (165 nm) measured by a humidified tandem differential mobility analyser (HTDMA); method D utilised size-dependent GFs measured at 35, 50, 75, 110 and 165 nm; method E divided the aerosol population into three hygroscopicity modes (near-hydrophobic, more-hygroscopic and sea-salt modes), and the total CCN number in each mode was cumulatively added up; method F used the full-size-scale GF probability density function (GF-PDF) in the most complex approach. The studied periods included high-biological-activity and low-biological-activity seasons in clean marine and polluted continental air masses to represent and discuss the most contrasting aerosol populations. Overall, a good agreement was found between estimated and measured N.sub.CCN with linear regression slopes ranging from 0.64 to 1.6. The temporal variability was captured very well, with Pearson's R value ranging from 0.76 to 0.98 depending on the method and air mass type. We further compared the results of using different methods to quantify the impact of size-dependent hygroscopicity and mixing state and found that ignoring size-dependent hygroscopicity induced overestimation of N.sub.CCN by up to 12 %, and ignoring a mixing state induced overestimation of N.sub.CCN by up to 15 %. The error induced by assuming an internal mixing in highly polluted cases was largely eliminated by dividing the full GF-PDF into three conventional hygroscopic modes, while assuming an internal mixing in clean marine aerosol did not induce significant error.