Express $140$ as a product of its prime factors.

Explain why $7 \times 11 \times 13+13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1+5$ are composite numbers.

Find the $LCM$ and $HCF$ of the following pairs of integers and verify that $LCM \times HCF =$ product of the two numbers $510$ and $92$.

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

Show that any positive odd integer is of the form $6q+1$,$6q+3$,or $6q+5$,where $q$ is some 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: $\frac{23}{2^{3} \times 5^{2}}$