Express $96$ as a product of prime factors.

The following real number is expressed in decimal form: $0.05005000500005 \ldots$. Determine whether it is rational or irrational. If it is rational,express it in the form of $\frac{p}{q}$.

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..........

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

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{15}{1600}$

Write the denominator of the rational number $\frac{257}{5000}$ in the form $2^{m} \times 5^{n},$ where $m, n$ are non-negative integers. Hence,write its decimal expansion,without actual division.