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Granite rocks are currently one of the foremost raw materials that can be used for various economic purposes such as ornamentation and building materials, because they do not possess radioactive concentrations and have good physical and mechanical properties. The granite rocks of north Um Taghir are connected to neoproterozoic rocks and integrated to the north Arabian-Nubian Shield (ANS), which lies in Northeast Africa. Inductively coupled plasma mass spectrometry (ICP-MS) and X-ray fluorescence analysis, concurrent to some statistical analysis, have been carried for major oxides and some trace elements to extract much fundamental information by following certain mathematical methods. The exposed granite rock units in north Um Taghir are classified into four rock units represented by tonalite, granodiorite, monzogranite, and alkali-feldspar granite which are cut by different types of dikes. The magma of tonalite and granodiorite is low-to-medium K calc-alkaline affinity, while the magma of monzogranite and alkali-feldspar granite is medium-to-high K calc-alkaline affinity, and of metaluminous to peraluminous nature. Granite rocks show a slightly depletion of fractionated patterns from light rare earth elements (LREEs) to heavy rare earth elements (HREEs) with slightly positive to negative Eu anomalies from tonalite to monzogranite and alkali-feldspar granites. The statistical criteria have been achieved to explore the significant differences of radiological hazard parameters among samples. It is obvious that there is no homogeneity among samples; furthermore, in Kruskal–Wallis test, Mann–Whitney test, and Pearson correlation coefficient, it can be noticed that there are significant differences between each pair of samples: tonalite, monzogranite; tonalite, alkali-feldspar granite; granodiorite, monzogranite; and granodiorite, alkali-feldspar granite. There is a strong direct relationship among granodiorite and both tonalite and alkali-feldspar granite, and among alkali-feldspar granite and tonalite and granodiorite. There is a strong inverse relationship among monzogranite and tonalite, granodiorite, and alkali-feldspar granite. As stated by all results, it can be mentioned that the granite rocks have a worthy result of mechanical and physical properties. So that they can be used for various economic purposes.