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Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10 −6 metre). Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted.
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. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
Many properties of a natural number n can be seen or directly computed from the prime factorization of n.. The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n.
If two or more factors of a polynomial are identical, then the polynomial is a multiple of the square of this factor. The multiple factor is also a factor of the polynomial's derivative (with respect to any of the variables, if several). For univariate polynomials, multiple factors are equivalent to multiple roots (over a suitable extension field).
A general-purpose factoring algorithm, also known as a Category 2, Second Category, or Kraitchik family algorithm, [10] has a running time which depends solely on the size of the integer to be factored. This is the type of algorithm used to factor RSA numbers. Most general-purpose factoring algorithms are based on the congruence of squares method.
Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms.
The number may be expressed as n = 50 − a so its square is (50−a) 2 = 50 2 − 100a + a 2. One knows that 50 2 is 2500. So one subtracts 100a from 2500, and then add a 2. For example, say one wants to square 48, which is 50 − 2. One subtracts 200 from 2500 and add 4, and get n 2 = 2304.
10 18: 1 square gigametre (Gm 2) 6.1 Gm 2: Surface area of the Sun [94] 10 19 30 Gm 2: Surface area of the star Vega: 10 20 100 Gm 2 10 21: 1 zetta square meter Z(m 2) 1 000 Gm 2: 10 22 11 000 Gm 2: Area swept by Mercury's orbit around the Sun 37 000 Gm 2: Area swept by Venus' orbit around the Sun 71 000 Gm 2: Area swept by Earth's orbit around ...