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

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: $\frac{13}{3125}$.

Use Euclid's division lemma to show that the cube of any positive integer is of the form $9m, 9m+1$ or $9m+8$.

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: $\frac{129}{2^{2} \cdot 5^{7} \cdot 7^{5}}$

Use Euclid's algorithm to find the $HCF$ of $4052$ and $12576$.