FactorInteger
Usage Message: FactorInteger[n] gives a list of the prime factors of the integer n, together with their exponents.
Attributes[FactorInteger] = {Listable, Protected} Options: FactorComplete
-> True GaussianIntegers
-> False Related Symbols Divisors
, DivisorSigma
, EulerPhi
, Prime
, PrimeQ
Notes: FactorInteger[n] returns a list of pairs {p,
k}, where p is a factor of n, and
k is the multiplicity of that factor. You can use Apply
to reconstruct the original integer from the result of FactorInteger.
In[1]:= result = FactorInteger[-39740679]
Out[1]= {{-1, 1}, {3, 3}, {11, 1}, {17, 2}, {463, 1}}
In[2]:= Times @@ Apply[Power, result, {1}]
Out[2]= -39740679
The algorithm used by FactorInteger uses trial division to remove small primes, and switches between the Pollard p-1, Pollard rho, and continued fraction algorithms for larger factors. Mathematically, integer factorization is only unique up to units. For example, although FactorInteger[-6] gives {{-1, 1}, {2, 1}, {3, 1}}, the result could in principle also be something like {{-2, 1}, {3, 1}} or {{-3, 1}, {2, 1}}. For positive integers, the only unit is {1, 1}, which is included in the list of factors only for FactorInteger[1]. (In Mathematica Version 2.2, FactorInteger returns {}.) For negative integers, Mathematica includes the unit {-1, 1} as the first element in the result. In Mathematica Version 3.0 there is an error in FactorInteger that can cause the kernel to crash if the multiplicity of one of the factors is greater than 2^16. This problem will be corrected for the next version of Mathematica. The solution to this problem is to temporarily create an expression (such as the result of Table[p, {2^16}] that includes at least 2^16 copies of the repeated factor.
Additional Online Documentation:
Mathematica 3.0
http://documents.wolfram.com/v3/RefGuide/FactorInteger.html
Mathematica 4.0
http://documents.wolfram.com/v4/RefGuide/FactorInteger.html
Questions or comments? Send email to support@wolfram.com.
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