Prime Factoring using a Visual Basic Module

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Primes are the building blocks of whole numbers and play a critical role in cryptography, signal processing, music theory, quantum mechanics, and many other fields.

How the Module Works

The VBA module stores the first 100 prime numbers in a "Prime" worksheet. It uses two loops:

1. FOR loop — iterates through the 100 primes one by one to find which can divide the input number. Terminates early once the number is fully factored to 1.
2. DO loop — for each prime that divides the input, keeps dividing until the prime no longer divides evenly. This handles repeated prime factors (e.g., 1,500 = 2 × 2 × 3 × 5 × 5 × 5).

Sub Factoring()
    Dim prime(1 To 100) As Integer, i As Integer
    Dim InputNbr As Long

    Sheets("Prime").Select
    Range("A3").Select

    For i = 1 To 100
        prime(i) = ActiveCell.Value
        ActiveCell.Offset(1, 0).Select
    Next i

    Sheets("Factoring").Select

    InputNbr = Range("InputNbr").Value

    Range("B5:B1000").Select
    Selection.ClearContents
    Range("B5").Select

    For i = 1 To 100
        If InputNbr = 1 Then
            Exit For
        End If

        Do While InputNbr Mod prime(i) = 0
            InputNbr = InputNbr / prime(i)
            ActiveCell.Value = prime(i)
            ActiveCell.Offset(1, 0).Select
        Loop
    Next i

    If InputNbr > 1 Then
        ActiveCell.Value = InputNbr
    End If
End Sub

Usage

1. Enter a whole number (no decimal places) in cell B3.
2. Click the Go! button to run the module.
3. The prime factors are listed starting from cell B5.

If the input number has no prime factors within the first 100 primes, the number itself appears as the result. If factoring requires primes beyond the first 100, the result may be incorrect — extend the prime list on the "Prime" worksheet to handle larger numbers.

The module currently processes one number at a time but can be extended with an additional loop to process a batch of inputs from a range.