Express $156$ as a product of its prime factors.

Use Euclid's division algorithm to find the $HCF$ of $196$ and $38220$.

Prove that $\sqrt{3}$ is irrational.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{13}{3125}$.

Prove that $6+\sqrt{2}$ is an irrational number.

There is a circular path around a sports field. Sonia takes $18$ minutes to drive one round of the field,while Ravi takes $12$ minutes for the same. Suppose they both start at the same point and at the same time,and go in the same direction. After how many minutes will they meet again at the starting point?