🔢 Math Calculator

📐 How It Works

Finds the largest number that divides both inputs without a remainder. The GCD is the basis of fraction simplification.

🔢 Worked Examples

• GCD(48, 18) = 6
• GCD(100, 75) = 25
• GCD(17, 13) = 1 (coprime)
• GCD(360, 144) = 72

📋 Common Use Cases

• Simplifying fractions to lowest terms
• Tiling problems — largest square tiles for a rectangular floor
• Cryptography — Euler's totient function
• Reducing ratios

💡 Did You Know?

The Euclidean algorithm is one of the oldest algorithms in existence (c. 300 BCE), and one of the most efficient. Even for very large numbers, it requires at most 5× the number of digits in the smaller number.

⚠️ Common Mistake

GCD(0, n) = n (not 0). Zero contributes no constraints, so the GCD is the other number.