Finding the prime factors

This lesson covers prime factorisation in VB.NET, with the aim of understanding a number-theory algorithm built on loops.

Prime factorisation breaks a number down into a product of primes. Testing divisibility from the smallest prime upwards, and dividing for as long as it divides, finds every prime factor.

The sample code starts at d = 2 and, while n divides by d, records the factor with factors.Add(d) and keeps dividing, increasing d by one when it no longer divides — repeating until n reaches 1.

A common early stumble is the nested loop structure. The outer loop increases the divisor d while the inner one keeps dividing for as long as it can — that two-stage arrangement is the key to understanding it.

Prime factorisation underpins cryptography such as RSA, which makes it a worthwhile way into number-theory algorithms.

📖 Reference code

Imports System.Collections.Generic

Module Program
    Function PrimeFactors(n As Integer) As List(Of Integer)
        Dim factors As New List(Of Integer)
        Dim d As Integer = 2
        Do While n > 1
            Do While n Mod d = 0
                factors.Add(d)
                n \= d
            Loop
            d += 1
        Loop
        Return factors
    End Function

    Sub Main()
        Console.WriteLine(String.Join(", ", PrimeFactors(60)))
        Console.WriteLine(String.Join(", ", PrimeFactors(97)))
    End Sub
End Module

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