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Documentation / Mathematica / Built-in Functions / Mathematical Functions / Number Theory /

FactorInteger

FilledSmallSquare FactorInteger[n] gives a list of the prime factors of the integer n, together with their exponents.

FilledSmallSquare Example: FactorInteger[2434500] LongRightArrow.

FilledSmallSquare For negative numbers, the unit {-1, 1} is included in the list of factors.

FilledSmallSquare FactorInteger also works on rational numbers. The prime factors of the denominator are given with negative exponents.

FilledSmallSquare FactorInteger[n, GaussianIntegers->True] factors over Gaussian integers.

FilledSmallSquare FactorInteger[m + I m] automatically works over the Gaussian integers.

FilledSmallSquare When necessary, a unit of the form {-1, 1}, {I, 1} or {-I, 1} is included in the list of factors.

FilledSmallSquare FactorInteger[n, FactorComplete->False] does fast but not necessarily complete factorization, and extracts only factors that are easy to find.

FilledSmallSquare See Section 1.1.3, Section 1.4.9 and Section 3.2.4.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: IntegerExponent, Prime, PrimeQ, Divisors.

FilledSmallSquare Related package: NumberTheory`FactorIntegerECM`.

FilledSmallSquare New in Version 1; modified in 5.0.

Further Examples