📊 GCD Finder
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📌 What is GCD?
The Greatest Common Divisor (GCD) of multiple numbers is the largest number that divides all of them without leaving a remainder.
Example: The GCD of 24, 36, and 48 is 12, since 12 is the largest number that divides all three numbers exactly.
📌 Methods to Calculate GCD
- Prime Factorization Method: Find the prime factors of each number and multiply the common factors.
- Division Method: Use repeated division to find the largest divisor common to all numbers.
- Euclidean Algorithm: Repeatedly subtract the smaller number from the larger until only one number remains.
📌 Examples of GCD Calculations
| Method | Example | Solution |
|---|---|---|
| Prime Factorization | 24, 36 | 24 = 2³ × 3, 36 = 2² × 3² → GCD = 2² × 3 = 12 |
| Division Method | 56, 98 | Divide 98 by 56 → remainder 42 → Divide 56 by 42 → remainder 14 → Divide 42 by 14 → remainder 0 → GCD = 14 |
| Euclidean Algorithm | 48, 18 | 48 – 18 = 30 → 30 – 18 = 12 → 18 – 12 = 6 → 12 – 6 = 6 → GCD = 6 |
❓ FAQs
Q1: How do I calculate the GCD?
✅ Use the prime factorization, division method, or Euclidean algorithm.
Q2: What is the difference between GCD and LCM?
✅ GCD is the largest common factor, while LCM is the smallest common multiple.
Q3: Can GCD be larger than the given numbers?
✅ No, GCD is always equal to or smaller than the smallest number.
Q4: Why is GCD important in real life?
✅ GCD is useful in simplifying fractions, optimizing resource distribution, and computing ratios.
Q5: Can I calculate GCD for more than two numbers?
✅ Yes, GCD can be found for multiple numbers using the same methods.