// Sample Code

// given n, define a boolean function that tells you whether a number is a
// factor of n and use that function to filter the array of numbers 1 to n
def factors(n : Int) = {
    def isFactor(m : Int) = n % m == 0
    (1 to n).toArray.filter(isFactor)
}

// By definition, a prime is a number greater than 2 whose only factors are 1
// and itself
def prime(n : Int) = factors(n).length == 2

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// Problem #1
// write a method named product that takes an array of integers
// (Array[Int]) as a parameter and returns the product of all
// the integers in the array.  You may assume the array contains
// at least 1 number.

// def product(ints : Array[Int]) =

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// Problem #2
// write a method named largestPrime that takes an array of integers
// (Array[Int]) as a parameter and returns the value of the largest
// prime in the array. You may assume the array contains at least
// 1 prime number.
// HINT: the prime method is helpful

// def largestPrime(ints : Array[Int]) =

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// Problem #3
// write a method named retainMultiples that takes an array of integers
// (Array[Int]) as a parameter and returns an array identical to the
// parameter, except this array will contain only elements which are
// multiples of another element in the array.  For this problem, a number
// is not a multiple of itself (so, 4 is the smallest multiple of 2).
// For example, if given an array containing 3, 4, 2, 5, and 8, then the
// result would be an array containing 4 and 8 (4 is a multiple of 2,
// and 8 is a multiple of both 2 and 4).  The 3, 2, and 5 are removed
// because they aren't multiples of any element in the array

// def retainMultiples(ints : Array[Int]) =

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// uncomment these lines of code to test your methods
var array = Array(3, 4, 2, 5, 8)
// var productResult = product(array) // correct: 960
// var largestPrimeResult = largestPrime(array) // correct: 5
// var retainMultiplesResult = retainMultiples(array) // correct: Array(4, 8)