According to Euclid's division lemma,for given positive integers $a$ and $7$,there exist unique non-negative integers $q$ and $r$ such that $a = 7q + r$; where..........

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{77}{210}$

$A$ sweet seller has $420$ Kaju burfis and $130$ Badam burfis. He wants to stack them in such a way that each stack carries the same number of items and they take up the least area of the tray. What is the maximum number of burfis that can be placed in each stack for this purpose?

Find the smallest five-digit number which is exactly divisible by $15$,$55$,and $99$.

Find the $\text{g.c.d.}$ of $867$ and $255$ using Euclid's division algorithm.

The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $18.484848 \ldots$