Real Numbers class 10

 In class IX, you began your exploration of the world of real numbers and encountered irrational numbers.we continue our discussion on real numbers in this chapter.we begin with our two very important properties of positive integers in section 1.2 and 1.

3 ,namely the Euclid's division algorithm and the fundamental theorem of arithmetic

Theorem 1.1: According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b.

The basis of the Euclidean division algorithm is Euclid’s division lemma. To calculate the Highest Common Factor (HCF) of two positive integers a and b we use Euclid’s division algorithm. HCF is the largest number which exactly divides two or more positive integers. That means, on dividing both the integers a and b the remainder is zero.