Find $g.c.d.$ of $210$ and $55$ by Euclid's algorithm.

Show that the square of an odd positive integer can be of the form $6q + 1$ or $6q + 3$ for some integer $q$.

Prove that $5^{n} \times 6^{n}$ ends in zero for any natural number $n \in N$.

Find the $g.c.d.$ (Greatest Common Divisor) of $155$ and $1385$ using Euclid's division algorithm.

Prove that the number $\sqrt{21}$ is irrational.

Using Euclid's division algorithm,find the largest number that divides $1251, 9377$ and $15628$ leaving remainders $1, 2$ and $3$,respectively.