State Euclid's division lemma and give some examples.

Foundation

Mathematics Foundation

Euclids Definitions Axioms and Postulates

HCF and LCM

Properties of Real Number

Question

State Euclid's division lemma and give some examples.

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State Euler’s division lemma and give some examples

Step,-1: Stating Euler’s division lemma

According to Euler’s division lemma, if we have two positive integers a and b, then there exist unique

{\text{integers q and r which satisfies the condition a,=,bq,+,r where 0}} \leqslant {\text{r &lt; b}}

Step,-2: Writing some examples

Consider two numbers 78 and 980,

We have, 980,=,78 \times 12,+,44

∴ Here, a,=,980, b,=,78, q,=,12, r,=,44

Similarly, a,=,675 and b,=,81

\Rightarrow 675,=,81 \times 8,+,27

Hence, Euclid’s division lemma is stated.