Factors Finder

Find all factors of any integer with interactive demo and code examples

What are Factors?

Factors are numbers we can multiply together to get another number. For example, factors of 12 are:

1 × 12 = 12
2 × 6 = 12
3 × 4 = 12

So the factors of 12 are 1, 2, 3, 4, 6, and 12.

This program finds all factors of a number entered by the user. We use the simple logic that a number is divisible by all its factors. In programming terms, if number % factor == 0, then the divisor is a factor.

Interactive Factors Finder

Enter any positive integer to find its factors:

How it works:

The algorithm checks divisibility from 1 to the square root of the number for efficiency. For each divisor found, both the divisor and the quotient are added to the factors list.

Code Examples

Visual Basic 6

This VB6 code finds factors and displays them in a list box.

Private Sub cmdFindFactors_Click()
    ' Clear previous results
    lstFactors.Clear
    
    ' Get the number from text box
    Dim num As Long
    num = Val(txtNumber.Text)
    
    ' Always include 1 and the number itself
    lstFactors.AddItem "1"
    
    ' Find factors from 2 to square root of num
    Dim i As Long
    For i = 2 To Sqr(num)
        If num Mod i = 0 Then
            lstFactors.AddItem CStr(i)  ' Add divisor
            ' Add quotient if it's different
            If i <> num \ i Then
                lstFactors.AddItem CStr(num \ i)
            End If
        End If
    Next i
    
    ' Add the number itself
    lstFactors.AddItem CStr(num)
    
    ' Sort the factors
    Call SortListBox(lstFactors)
    
    ' Show factor count
    lblCount.Caption = CStr(lstFactors.ListCount) & " factors found"
End Sub

VB.NET

Modern VB.NET implementation with efficient algorithm.

Private Sub btnFindFactors_Click(ByVal sender As System.Object, 
                                 ByVal e As System.EventArgs) Handles btnFindFactors.Click
    
    ' Clear previous results
    lstFactors.Items.Clear()
    
    ' Parse input number
    Dim number As Long
    If Not Long.TryParse(txtNumber.Text, number) Or number < 1 Then
        MessageBox.Show("Please enter a valid positive integer")
        Return
    End If
    
    ' Create a list to store factors
    Dim factors As New List(Of Long)
    
    ' Add 1 and the number itself
    factors.Add(1)
    If number > 1 Then
        factors.Add(number)
    End If
    
    ' Find factors from 2 to square root of number
    Dim limit As Long = Math.Sqrt(number)
    For i As Long = 2 To limit
        If number Mod i = 0 Then
            factors.Add(i)  ' Add divisor
            ' Add quotient if it's different
            Dim quotient As Long = number \ i
            If quotient <> i Then
                factors.Add(quotient)
            End If
        End If
    Next
    
    ' Sort and display factors
    factors.Sort()
    lstFactors.DataSource = factors
    lblCount.Text = $"{factors.Count} factors found"
    
    ' Check if prime
    If factors.Count = 2 Then
        lblPrime.Visible = True
    Else
        lblPrime.Visible = False
    End If
End Sub

Algorithm Explanation

The most efficient way to find all factors of a number is to iterate only up to the square root of the number. This approach has O(√n) time complexity compared to O(n) for a naive approach.

Key Insight

If a number n has a factor i, then n/i is also a factor.

Efficiency

For n = 1,000,000, we only need 1,000 checks instead of 1,000,000.

Pseudocode

1. Add 1 to factors
2. For i from 2 to √n:
- If n % i == 0, add i and n/i
3. Add n

Exercise: Prime Number Checker

Modify the factors finder to also determine if the number is prime. A prime number has exactly two distinct factors: 1 and itself.

Hint: After finding all factors, check if the count is 2.