Express $404$ as a product of primes.

If a positive integer is of the form $3q + 1$,where $q$ is a natural number,then its square can be written in the form $3m + 1$. Is the statement true or false?

Express the number $7429$ as a product of its prime factors.

From the given factor tree, find the values of $x$ and $y$ respectively, assuming $x$ branches into $2$ and $5$, and $y$ branches into $x$ and $2$.

Show that the cube of any positive integer is of the form $4m, 4m+1$ or $4m+3$ for some integer $m$.

Check whether $4^n$ can end with the digit $0$ for any positive integer $n$.