# Factorisation

Nemo provides a unified interface to handle factorisations using the Fact objects. These can only be constructed using the factor function for the respective ring elements. This is best illustrated by an example.

julia> fac = factor(ZZ(-6000361807272228723606))
-1 * 2 * 229^3 * 43669^3 * 3

julia> unit(fac)
-1

julia> -6000361807272228723606 == unit(fac) * prod([ p^e for (p, e) in fac])
true

julia> for (p, e) in fac; println("$p$e"); end
2 1
229 3
43669 3
3 1

julia> 229 in fac
true

julia> fac[229]
3

### Basic functionality

Objects of type Fac are iterable, that is, if a is an object of type Fac, then for (p, e) in a will iterate through all pairs (p, e), where p is a factor and e the corresponding exponent.

Base.inMethod
in(a, b::Fac)

Test whether $a$ is a factor of $b$.

Base.getindexMethod
getindex(a::Fac, b) -> Int

If $b$ is a factor of $a$, the corresponding exponent is returned. Otherwise an error is thrown.

Base.lengthMethod
length(a::Fac) -> Int

Return the number of factors of $a$, not including the unit.