The prime factorization of $30$ can be written as:

The decimal expansion of $\frac{13}{3125}$ is:

Prove that one and only one out of $n, n+2$ and $n+4$ is divisible by $3,$ where $n$ is any positive integer.

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: $\frac{29}{343}$.

Without performing long division,state whether the decimal expansion of the rational number $\frac{13}{3125}$ is terminating or non-terminating repeating.

Show that any positive odd integer is of the form $6q+1$,$6q+3$,or $6q+5$,where $q$ is some integer.