Express $5005$ as a product of its prime factors.

An army contingent of $616$ members is to march behind an army band of $32$ members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Write down the decimal expansion of the rational number $\frac{29}{343}$.

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: $\frac{17}{8}$.

Find the $LCM$ and $HCF$ of the following pairs of integers and verify that $LCM \times HCF =$ product of the two numbers $26$ and $91$.

Prove that $\sqrt{5}$ is irrational.