🎯 About GCD/HCF Calculator
The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF), is the largest positive integer that divides all given numbers without a remainder.
Our calculator finds the GCD for 2 to 5 numbers using three different methods: Euclidean Algorithm, Prime Factorization, and Listing Factors.
📝 How to Use
- Choose how many numbers (2 to 5)
- Enter your numbers in the input fields
- Click "Calculate GCD"
- View results with three different solution methods
- See practical applications and properties
🔍 Calculation Methods
Method 1: Euclidean Algorithm (Most Efficient)
- Divide the larger number by the smaller
- Replace larger with smaller, smaller with remainder
- Repeat until remainder is 0
- Last non-zero remainder is the GCD
Method 2: Prime Factorization
- Break each number into prime factors
- Find common prime factors
- Take the lowest power of each common prime
- Multiply them together
Method 3: Listing Factors
- List all factors of each number
- Find common factors
- The largest common factor is the GCD
💡 Common Uses
- Simplifying Fractions: Divide numerator and denominator by GCD
- Problem Solving: Finding largest equal groups
- Tiling Problems: Largest tile size that fits perfectly
- Cryptography: Essential in RSA encryption
- Music Theory: Finding common time signatures
📚 Examples
2 Numbers:
- GCD(12, 18) = 6
- GCD(24, 36) = 12
- GCD(15, 25) = 5
3 Numbers:
- GCD(12, 18, 24) = 6
- GCD(20, 30, 40) = 10
Real-World Example:
You have 24 apples and 36 oranges. What's the largest number of identical fruit baskets you can make?
Answer: GCD(24, 36) = 12 baskets (each with 2 apples and 3 oranges)
✨ Key Features
- Calculate GCD for 2-5 numbers
- Three different solution methods
- Step-by-step detailed explanations
- Shows GCD × LCM relationship
- Fraction simplification examples
- Visual factor highlighting
- Educational and practical