Project Euler 03. Largest prime factor with Scala

Problem Definition

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

What is the largest prime factor of the number 600851475143?

Source: https://projecteuler.net/problem=3

Solution

object Euler03 {

  type Factor = Long
  type Number = Long
  type Factors = List[Factor]

  /* Returns the largest prime factor of the given
   * number.It first computes all the prime factors of the given
   * number and then returns the largest among them.
   */
  def largestPrimeFactor (x: Number): Factor = 
    primeFactors(x).max


  /* Returns the prime factors of the given number x. For instance
   * if the number x equals to 5, it returns List(2,3).
   */
  def primeFactors(x: Number): Factors = {
    val numUpToSqrt = (2L to math.sqrt(x).toLong)
    val divisibleBy = numUpToSqrt.find(x % _ == 0)

    divisibleBy match {
      case None =>  List(x) 
      // x is a prime number and not divisible by any
      case Some(d) => d :: primeFactors(x/d)
    }
  }
}

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