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Theorem: Fundamental Theorem of Arithmetic Explained with Examples – CBSE Class 10 Maths Notes
Class 10 Maths – Theorem : Fundamental Theorem of Arithmetic 🧠What Does the Theorem Say? " Every composite number can be expressed (factorised) as a product of prime numbers, and this factorisation is unique , apart from the order of the prime factors. " ✅ Let’s Break It Down: A composite number is a natural number that is not prime and has more than two factors . According to the theorem: Every composite number can be written as a product of prime numbers . This factorisation is unique , except for the order in which the primes are written. 🔢 Example Take the number 32760 We can write: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13 = 2³ × 3² × 5 × 7 × 13 Now, whether you write it as: 2 × 3 × 5 × 7 × 13 × 2 × 3 × 2 or 3 × 2 × 2 × 5 × 7 × 3 × 2 × 13 👉 It doesn’t matter — it’s still the same set of prime numbers multiplied together. ✅ That’s what “ unique, except for order ” means. 💡 Important Notes A prime factorisation is a way to express a ...
The Story of the Fundamental Theorem of Arithmetic: From Euclid’s Elements to Gauss’s Genius
Story: "The Secret Code of Numbers – From Euclid to Gauss" “Behind every number lies a hidden code. One that only the greatest minds in history could fully understand...” 🌿 Chapter 1: The Ancient Whisper – Euclid’s Discovery It all began more than 2,000 years ago in the great library of Alexandria , where a wise Greek mathematician named Euclid was writing his famous book – The Elements . In Book IX, Proposition 14 , Euclid hinted at something amazing: "Every number is built from primes… like bricks building a wall." But he didn’t call it a "theorem." He didn’t even prove it the way we do now. It was more like a quiet whisper from the past – a mystery waiting to be unlocked. 👑 Chapter 2: Enter the Prince of Mathematicians – Carl Friedrich Gauss Fast forward to the year 1801 in Germany. A young genius named Carl Friedrich Gauss , only 24 years old , published his masterpiece: 📘 Disquisitiones Arithmeticae — a powerful book that changed...



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