HCF Calculator with Prime Factorization Steps

Find the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of any set of numbers with our intuitive and educational calculator. This tool goes beyond just giving you an answer; it provides a detailed, step-by-step breakdown using the prime factorization method. It's the perfect tool for students learning about number theory and for anyone who needs to understand the "why" behind the HCF.

How It Works

Our calculator is designed to be interactive and transparent, showing you the full calculation process in real-time.

  1. Enter Your Numbers: Type a number using the on-screen keypad or your keyboard and click "Add" to include it in the list.
  2. Build Your List: Add at least two numbers to the list. You can easily remove a number by clicking the '×' on its pill.
  3. Analyze the Results: The HCF is calculated and displayed instantly. Below, a detailed breakdown shows exactly how the answer was derived using prime factorization.

Key Features

  • HCF for Multiple Numbers: Calculate the Highest Common Factor for a list of two or more positive integers.
  • Detailed Step-by-Step Breakdown: This is more than a simple calculator. It teaches the prime factorization method by showing:
    • The complete prime factorization of every number you enter (e.g., `90 = 2 × 3² × 5`).
    • The common prime factors and their lowest powers across all numbers.
    • The final HCF calculation as a product of these common factors, providing a clear path to the solution.
  • Real-Time Calculation: The HCF and the entire step-by-step breakdown update instantly as you add or remove numbers from your list.
  • Interactive Number List: Your entered numbers are displayed as "pills" that can be individually removed at any time, allowing for quick adjustments to your calculation.
  • Dual Input Methods: Use the convenient on-screen keypad for touch devices or take advantage of full keyboard support (including Enter, Backspace, and Escape) for fast entry.

How to Use the Calculator

  1. Step 1: Enter a Number
    Use the keypad or your keyboard to type a number into the input display.
  2. Step 2: Add to List
    Click the "Add" button or press Enter/Space to add the number to the calculation list.
  3. Step 3: Repeat for All Numbers
    Continue adding all the numbers for which you want to find the HCF.
  4. Step 4: Review the Breakdown
    Once you have at least two numbers, the final HCF will appear at the top, and the "Calculation Breakdown" section below will show the detailed prime factorization steps.

Find Our Tool

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