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In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted (,).
A least common multiple of a and b is a common multiple that is minimal, in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]
Another definition of the GCD is helpful in advanced mathematics, particularly ring theory. [12] The greatest common divisor g of two nonzero numbers a and b is also their smallest positive integral linear combination, that is, the smallest positive number of the form ua + vb where u and v are integers.
Any two elements of a UFD have a greatest common divisor and a least common multiple. Here, a greatest common divisor of a and b is an element d that divides both a and b, and such that every other common divisor of a and b divides d. All greatest common divisors of a and b are associated. Any UFD is integrally closed.
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients).
hcf – highest common factor of two numbers. (Also written as gcd.) H.M. – harmonic mean. HOL – higher-order logic. Hom – Hom functor. hom – hom-class. hot – higher order term. HOTPO – half or triple plus one. hvc – havercosine function. (Also written as havercos.) hyp – hypograph of a function.
In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions ...