Factoring Calculator

How the Calculator Works:

1. User Input:

   • Enter a positive integer in the input field.
   • The calculator validates the input to ensure it’s a valid number (non-negative integer).

2. Factor Calculation:

   • The calculator identifies all divisors of the given number by iterating from 1 to the square root of the number.
   • For each divisor $d$ found, both $d$ and the quotient $n/d$ (where $n$ is the original number) are identified as factors.
   • The calculator then sorts and displays all factors in ascending order.

3. Factor Pairs:

   • Each divisor $d$ is paired with $n/d$ to form factor pairs, which are displayed in the format $d \times (n/d) = n$.

4. Output:

   • The calculator displays both the total number of factors and the corresponding factor pairs.

Formula:

The factors of a number $n$ are all the integers $d$ such that:

$$n \% d = 0$$

Where:

• $n$ is the input number.
• $d$ is a divisor of $n$.
• $n \% d$ is the modulus operator, which gives the remainder when $n$ is divided by $d$.

The factor pairs are the combinations of factors $d$ and $n/d$ that satisfy:

$$d \times (n/d) = n$$

Where:

• $d$ is a divisor of $n$.
• $n/d$ is the quotient of $n$ divided by $d$.

Example Calculations:

Example 1: Factors of 36

Input:

• $n = 36$

Factor Calculation:

• Divisors of 36: $1, 2, 3, 4, 6, 9, 12, 18, 36$
  

Factor Pairs:

• $1 \times 36 = 36$
  
• $2 \times 18 = 36$
  
• $3 \times 12 = 36$
  
• $4 \times 9 = 36$
  
• $6 \times 6 = 36$
  

Output:

• The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
• The factor pairs of 36 are:
  • $1 \times 36 = 36$
    
  • $2 \times 18 = 36$
    
  • $3 \times 12 = 36$
    
  • $4 \times 9 = 36$
    
  • $6 \times 6 = 36$
    

Example 2: Factors of 100

Input:

• $n = 100$
  

Factor Calculation:

• Divisors of 100: $1, 2, 4, 5, 10, 20, 25, 50, 100$
  

Factor Pairs:

• $1 \times 100 = 100$
• $2 \times 50 = 100$
  
• $4 \times 25 = 100$
  
• $5 \times 20 = 100$
  
• $10 \times 10 = 100$
  

Output:

• The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
• The factor pairs of 100 are:
  • $1 \times 100 = 100$
    
  • $2 \times 50 = 100$
    
  • $4 \times 25 = 100$
    
  • $5 \times 20 = 100$
    
  • $10 \times 10 = 100$