Real number chapter 1 CBSE class 10th
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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 ...
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