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

What is the largest prime factor of the number 600851475143 ?

Solution:
Function Prob003() As Long
Dim Src As Long = 600851475143
Dim PrimeCol As New Collection
For tmpVal As Long = 2 To Src
If tmpVal > System.Math.Sqrt(Src) Then Exit For
If IsPrime(tmpVal) = True Then
PrimeCol.Add(tmpVal)
End If
Next
For k As Integer = 1 To PrimeCol.Count
If Src Mod PrimeCol(k) = 0 Then
If PrimeCol(k) > Prob003 Then Prob003 = PrimeCol(k)
End If
Next
End Function

Summary:
This one was kind of a pain. I had forgotten a lot about what makes a prime and the various rules, tricks, etc. when dealing with them…

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

Solution:
Function Prob002() As Long
Dim Term1 As Long = 1
Dim Term2 As Long = 2
Dim tmpTerm As Long = 0
While Term1 < = 4000000 If Term1 Mod 2 = 0 Then Prob002 += Term1 tmpTerm = Term1 + Term2 Term1 = Term2 Term2 = tmpTerm End While End Function

Summary:
Even though it'll never be as exciting as in the movie Pi, I do love working with Fibonacci sequences.

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

Solution:
Function Prob001() As Integer
For k As Integer = 3 To 999
If k Mod 3 = 0 OrElse k Mod 5 = 0 Then Prob001 += k
Next
End Function

Summary:
Easy-peasy.