Solution

$${\textbf{State Euler's division lemma and give some examples}}$$
$${\textbf{Step -1: Stating Euler's division lemma}}$$
$${\text{According to Euler's division lemma, if we have two positive integers a and b, then there exist unique}}$$
$${\text{integers q and r which satisfies the condition a = bq + r where 0}} \leqslant {\text{r < b}}$$
$${\textbf{Step -2: Writing some examples}}$$
$${\text{Consider two numbers 78 and 980,}}$$
$${\text{We have, 980 = 78}} \times {\text{12 + 44}}$$
$$\therefore {\text{ Here, a = 980, b = 78, q = 12, r = 44}}$$
$${\text{Similarly, a = 675 and b = 81}}$$
$$ \Rightarrow {\text{ 675 = 81}} \times {\text{8 + 27}}$$
$$\textbf{Hence, Euclid's division lemma is stated.}$$