Real Numbers
- Euclid’s Division Lemma : Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 ≤ r < b.
- The Fundamental Theorem of Arithmetic : Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique except for the order in which this prime factors occur.
- For any two positive integers a and b,HCF (a, b) × LCM (a, b) = a × b.
- For any three positive integers a, b and c, we have haveHCF (a, b, c) =(a x b x c x LCM (a, b, c))/(LCM (a, b) x LCM (b, c) x LCM (a, c)) Also, note that, HCF (a, b, c) × LCM (a, b, c) ≠ a × b × c.
- Let a be a positive integer and p be a prime number such that p dividesa2, then p alsodivides a.
- If p is a positive prime, then√p is an irrational number. For example √2, √3, √5… are irrational numbers.
- A positive integer p is prime, if it is not divisible by any prime less than or equal to √p.
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