Public Function Factoral(n As Integer) As Double
 If n < 1 OrElse n > 170 Then Return 0
 ' Factoral of 171 is larger than Double.maxvalue
 Dim ret As Double = 1
 For i As Integer = 1 To n
  ret *= i
 Next
 Return ret
End Function
'
Private Function Factorize(n As Integer) As List(Of Integer)
 ' Prime numbers will return an empty list
 ' List never includes 1 or the number
 ' This works for numbers between +2 and Integer.MaxValue (+2,147,483,647)
 ' However, this method is not suitable for testing huge numbers.
 Dim listFactors As New List(Of Integer)
 Dim sqrtOfN As Integer = CInt(Math.Ceiling(Math.Sqrt(n)))
 While n Mod 2 = 0
  n \= 2
  listFactors.Add(2)
 End While
 For i As Integer = 3 To sqrtOfN Step 2
  While n Mod i = 0
   n \= i
   listFactors.Add(i)
  End While
  If i > n OrElse i > sqrtOfN Then
   Exit For
  End If
 Next
 Return listFactors
End Function
'
Private Shared Function GreatestCommonFactor(a As Integer, b As Integer) As Integer
 Dim temp As Integer
 While b <> 0
  temp = b
  b = a Mod b
  a = temp
 End While
 Return a
End Function
'
Private Function LowestCommonMultiple(a As Integer, b As Integer) As Integer
 Dim temp, a1, b1 As Integer
 a1 = a
 b1 = b
 While b1 <> 0
  temp = b1
  b1 = a1 Mod b1
  a1 = temp
 End While
 Return a * b \ a1
End Function
  

Public Function Permutation(num1 As Integer, num2 As Integer) As Long
 Dim temp As Integer = num1
 Dim ret As Long = 1
 If num1 > num2 Then
  num1 = num2
  num2 = temp
 End If
 If num1 < 1 OrElse num2 < 1 Then Return 0
 For i As Integer = num1 To num2
  ret *= i
 Next
 Return ret
End Function
'
Private Function IsPrime(n As Integer) As Boolean
 ' This works for numbers between +2 and Integer.MaxValue (+2,147,483,647)
 ' There is mathematical debate as to whether 0 and 1 are Prime Numbers
 ' This method is not suitable for testing huge numbers.
 If n < 3 Then Return True
 If n Mod 2 = 0 Then Return False
 Dim primeNumber As Boolean = True
 For i = 3 To Math.Floor(Math.Sqrt(n)) Step 2
  If n Mod i = 0 Then
   primeNumber = False
   Exit For
  End If
 Next
 Return primeNumber
End Function
'
Private Function ListAllPrimes(max As Integer) As List(Of Integer)
 ' note - large values for max (> about 10000) will need to be run in background to avoid risk of timeout errors
 ' very large values for max (> about 1000000) may not complete in a realistic timescale!
 Dim ret As New List(Of Integer)
 Dim prime As Boolean
 For i As Integer = 3 To max Step 2
  prime = True
  For Each p As Integer In ret
   If i Mod p = 0 Then
    prime = False
    Exit For
   End If
  Next
  If prime Then
   ret.Add(i)
  End If
 Next
 If max >= 2 Then ret.Insert(0, 2)
 Return ret
End Function
  

Public Function Combination(num1 As Integer, num2 As Integer) As Long
 Dim temp As Integer = num1
 If num1 > num2 Then
  num1 = num2
  num2 = temp
 End If
 If num1 < 1 OrElse num2 < 1 Then Return 0
 Return Factoral(num2) / (Factoral(num1) * Factoral(num2 - num1))
End Function
  

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