Question

state Euclid division Lemma how this Lemma is helpful in various application related to our day to day life

Answer 1

 Euclid’s Division Lemma if we have two positive integers a and b, then there exists unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.

The basis of 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. By exactly we mean that on dividing both the integers a and b the remainder is zero

Answer 2

Euclid division lemma : given positive integer's a and b such that there exists unique pair of integers q and r satisfying a=bq+r(0<r<b)