Using Euclid's division algorithm,determine whether the pair of numbers $231$ and $396$ are co-prime.

Prove that the following number is irrational: $\sqrt{11}$

Prove that $n^{2}-n$ is divisible by $2$ for every positive integer $n$.

"The product of three consecutive positive integers is divisible by $6$". Is this statement true or false? Justify your answer.

$A$ rational number in its decimal expansion is $327.7081$. What can you say about the prime factors of $q$,when this number is expressed in the form $\frac{p}{q}$? Give reasons.

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{13}{3125}$