We determined the cosmic-ray produced noble gas abundances in eight diogenites, four eucrites, and four howardites. Using these and additional noble gas and chemical data from the literature, composition and shielding dependent production rates of achondrites for 3 He, 21 Ne, 38 Ar, 78 Kr, 83 Kr, and 126 Xe were derived based on 81 KrKr exposure ages. The cosmogenic ratio 22 Ne/ 21 Ne is found to be a valid shielding indicator for all howardites, eucrites, and diogenites (HEDs). This ratio correlates with other shielding dependent ratios, such as 78 Kr/ 83 Kr, 80 Kr/ 83 Kr, 124 Xe/ 131 Xe, 126 Xe/ 131 Xe, and 128 Xe/ 131 Xe. We show that strong correlations for these ratios also exist for basaltic lunar rocks. The new production rates were used for the calculation of exposure ages for all HEDs with known noble gas abundances. Two major exposure age clusters at 21 Ma and 38 Ma are observed in all three classes. We find that five asteroid break-up events, characterized by exposure ages 6 ± 1 Ma, 12 ± 2 Ma, 21 ± 4 Ma, 38 ± 8 Ma, and 73 ± 3 Ma produced all diogenites, fifteen out of seventeen howardites, and twenty-eight out of thirty-nine eucrites. We conclude that asteroidal or cometary impact events at such times on one or several parent bodies are responsible for the ejection of eucrites, howardites, and diogenites. Probable parent bodies are multiple 4 Vesta-derived kilometer-sized objects of basaltic achondritic composition reaching the 3:1 resonance region, a proposed source area for meteorites. The direct ejection from Vesta and capture by Earth of basaltic meteorites has been shown to be dynamically difficult. In such a scenario large events 38 Ma and 21 Ma ago are required, liberating simultaneously material representing Vesta's surface (eucrites, howardites) and interior regions (diogenites).