In this Chapter, you have studied the following points of Real Numbers Class 10 Maths:
1. Euclid’s division lemma :

Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 ≤ r < b.
2. Euclid’s division algorithm : This is based on Euclid’s division lemma. According to this, the HCF of any two positive integers a and b, with a > b, is obtained as follows:
Step 1 : Apply the division lemma to find q and r where a = bq + r, 0 ≤ r < b.
Step 2 : If r = 0, the HCF is b. If r ≠ 0, apply Euclid’s lemma to b and r.
Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be HCF (a, b). Also, HCF(a, b) = HCF(b, r).
3. The Fundamental Theorem of Arithmetic :

Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
4. If p is a prime and p divides a2 , then p divides a, where a is a positive integer.

Select Lecture

  • Number Systems
  • Euclid’s Division Lemma
  • Euclid’s Division Algorithm
  • HCF / GCD
  • Uses of Euclid’s Division Lemma other then finding HCF / GCD