#### Problem

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

#### Solution

open System let findFactorsOf(n:int64) = let upperBound = int64(Math.Sqrt(double(n))) [2L..upperBound] |> Seq.filter (fun x -> n % x = 0L) let isPrime(n:int64) = findFactorsOf(n) |> Seq.length = 0 let findMaxPrimeFactorOf(n:int64) = let upperBound = int64(Math.Sqrt(double(n))) [2L..upperBound] |> Seq.filter (fun x -> n % x = 0L) |> Seq.filter isPrime |> Seq.max let maxPrime = findMaxPrimeFactorOf(600851475143L)

As this solution requires a bit more work, I created two helper functions *findFactorsOf* and *isPrime*, and as you’ve probably noticed, I had explicitly declare that the value *n* should be a *int64* type:

let findFactorsOf(n:int64)

That’s because the number 600851475143 in the problem is outside of the range of the *int32* type so all the functions must be able to work with a *int64* type. This is one of few cases where you can’t just rely on the type inference in F#.

Another thing you might have noticed is that the syntax for casting in F# is *type(value)*, e.g.

int64(n)

as opposed to the syntax in C#:

(long)n

And did you notice that I used the Math.Sqrt method in my solution? That’s right, you can use any CLR types in F# just as you can in C#! In order to import a namespace in F#, you need to use the open keyword:

open System

which is equivalent to the using directive in C#:

using System

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