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common factor
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common factor

Number that will divide two or more others without leaving a remainder. For example, the factors of 8 are 1, 2, 4, and 8; the factors of 12 are 1, 2, 3, 4, 6 and 12; and the factors of 16 are 1, 2, 4, 8 and 16. The numbers 2 and 4 are factors of all three numbers (8, 12, and 16) and are known as the common factors; 4 is known as the highest common factor. A prime number can only have factors of one and itself.
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He describes rings and fields, including linear equations in a field and vector spaces, polynomials over a field, factorization into primes, ideals and the greatest common divisor, solution of the general equation of nth degree, residual classes, extension fields, and isomorphisms.
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In section II (24 pages) Gauss proves the uniqueness of the factorisation of integers into primes and defines the concepts of greatest common divisor and least common multiple.
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