FactorInt

FactorInt[ n ] returns the prime factorisation of a positive integer.

Usages

`FactorInt[ n ]`

FactorInt[ n ] returns a list {primes, exponents}, such that n is the product of each prime to the power of its exponent. n must be a positive integer.

Example	in	out
`90 = 2¹ · 3² · 5¹`.	`FactorInt[ 90 ]`	`{ {2, 3, 5}, {1, 2, 1} }`
A script variable.	`x := 35 r := FactorInt[x]`	`r = { {5, 7}, {1, 1} }`
A prime number.	`FactorInt[ 17 ]`	`{ {17}, {1} }`
`1` has no prime factors.	`FactorInt[ 1 ]`	`{ {}, {} }`

`FactorInt[ list ]`

If the argument is a list, each element is factorised.

Example	in	out
Factorise two numbers.	`FactorInt[ {12, 15} ]`	`{ { {2, 3}, {2, 1} }, { {3, 5}, {1, 1} } }`

Details

Calculated numbers: the argument must already be a number. In a script, FactorInt[ 3*17 ] is left unevaluated, because 3*17 is not calculated. Use FactorInt[ CalcTimes[3, 17] ] instead.
Large numbers: numbers larger than 10²¹ are left unevaluated.

Invalid input	Result
`FactorInt[ 0 ]`, `FactorInt[ -12 ]`	Left unevaluated: `n` must be positive.
`FactorInt[ 2.5 ]`, `FactorInt[ x ]`	Left unevaluated: `n` must be an integer.

Warning

The primes are not always in ascending order. For example, FactorInt[ 51 ] returns { {17, 3}, {1, 1} }. If you need them in order, sort them with SortI:
F := FactorInt[1938] I := SortI[F[[1]]] P := Map[i -> F[[1]][[i]], I] E := Map[i -> F[[2]][[i]], I]
gives P = {2, 3, 17, 19} and E = {1, 1, 1, 1}.
Prime factors larger than about 2·10⁹ are not handled correctly and give a wrong result.

See also: CalcDivisors, CalcGcd, SortI