NCERT Class 10 Maths Real Numbers Questions

• Euclid’s Division Lemma : Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.

• Euclid’s Division Algorithm to obtain the HCF of two positive integers, say c and d, c > d.

Step 1 : Apply Euclid’s division lemma to c and d, to find whole numbers q and r, such that c = dq + r, 0 ≤ r < d.

Step 2 : If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.

Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.

• Fundamental Theorem of Arithmetic : Every composite number can be expressed as a product of primes, and this expression (factorisation) is unique, apart from the order in which the prime factors occur.

• Let p be a prime number. If p divides a2, then p divides a, where a is a positive integer.

• √2 ,  √3 ,  √5 are irrational numbers.

• The sum or difference of a rational and an irrational number is irrational.

• The product are quotient of a non-zero rational number and an irrational number is irrational. • For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.

Please refer to attached file for NCERT Class 10 Maths Real Numbers Questions