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Based on existing knowledge about the greatest common divisor of integers in combination with matrix results on the primary domain, the article clarifies definition of greatest common divisor of square matrices, proving the existence of the greatest common divisor of the square matrices on the main domain, detailing how to find the greatestTDMU, số 2 (27) – 2016 common divisor of two square matrices with elements as integers, and proving some properties of the divisor and the greatest common divisor of square matrices