Use Euclid's division algorithm to find the $HCF$ of $196$ and $38220$.

Find the $HCF$ of $96$ and $404$ by the prime factorisation method. Hence,find their $LCM$.

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: $\frac{23}{2^{3} \times 5^{2}}$

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

Express $156$ as a product of its prime factors.

Show that $3 \sqrt{2}$ is irrational.