🔢 HCF Calculator
HCF result will appear here…
📌 Understanding HCF (GCD)
The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two integers is the largest integer that divides both numbers without leaving a remainder.
- Euclidean Algorithm: Uses repeated division (iterative or recursive) to find the HCF.
- Prime Factorization: Factors each number into primes and multiplies the common factors.
📌 Examples of HCF Calculation
| Number 1 | Number 2 | HCF | Method |
|---|---|---|---|
| 48 | 18 | 6 | Euclidean |
| 100 | 80 | 20 | Euclidean |
| 35 | 28 | 7 | Prime Factorization |
🔧 Practical Applications of HCF
1. Simplifying Fractions: The HCF is used to reduce fractions to their simplest form.
2. Problem Solving: It plays a key role in number theory and algebraic problems.
3. Real-World Scenarios: Useful in areas such as cryptography and signal processing.
❓ FAQs
Q1: What is the HCF?
✅ The HCF (or GCD) is the largest positive integer that divides two or more integers without a remainder.
Q2: Which method is the fastest?
✅ The Euclidean algorithm (iterative or recursive) is very efficient. The prime factorization method is more intuitive but can be slower for large numbers.
Q3: Can I use this calculator for negative numbers?
✅ This calculator is designed for positive integers only.
Q4: What is the difference between iterative and recursive methods?
✅ The iterative method uses a loop to repeatedly calculate the remainder, whereas the recursive method calls itself until the base case is reached.
Q5: When should I use prime factorization?
✅ Prime factorization is useful for understanding the factors of a number but is generally best for smaller integers.
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