Find the $LCM$ and $HCF$ of the following integers by applying the prime factorisation method: $17, 23$ and $29$.

Show that every positive even integer is of the form $2q$,and that every positive odd integer is of the form $2q+1$,where $q$ is some integer.

Use Euclid's division algorithm to find the $HCF$ of $135$ and $225$.

Determine whether the rational number $\frac{77}{210}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

Write down the decimal expansion of the rational number $\frac{17}{8}$.

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: $\frac{15}{1600}$.