Question

Prov Euclid's Division Lemma.

Answer 1

Answer:

Euclid’s division lemma:

Euclid’s division lemma, states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that a = b × q + r where 0 ≤ r < b.

Euclid’s division lemma can be used to find the highest common factor of any two positive integers and to show the common properties of numbers.

For a pair of given positive integers ‘a’ and ‘b’, there exist unique integers ‘q’ and ‘r’ such that

a = b q + r, where 0 ≤ r < b

Explanation:

Thus, for any pair of two positive integers a and b; the relation

a =bq + r , where 0 ≤ r < will be true where q is some integer.

 

Answer 2

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 comman 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 possitive integers . by exactly we mean that by dividing both the integers a and b the remainder is 0 .

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