with many .
For example, the factorization of 32851 is , more usually expressed as . Because of the commutative property of multiplication, it does not matter in what order the prime factors are stated in, but it is customary to give them in ascending order (http://planetmath.org/AscendingOrder), and to group them together by the use of exponents.
The factorization of a positive integer is unique (this is the fundamental theorem of arithmetic). For a negative number one could take the factorization of and randomly give negative signs to one (or any odd number) of the prime factors. Alternatively, the factorization can be given as (this is what Mathematica opts for).
The term “factorization” is often used to refer to the actual process of determining the prime factors. There are several algorithms to choose from, with trial division being the simplest to implement.
|Date of creation||2013-03-22 16:39:09|
|Last modified on||2013-03-22 16:39:09|
|Last modified by||PrimeFan (13766)|