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

Find the $\mathrm{HCF}$ and $\mathrm{LCM}$ of $120$ and $90$ by prime factorisation method.

Find the $\mathrm{HCF}$ and $\mathrm{LCM}$ of $50$ and $60$ by prime factorisation method.

Find the $\mathrm{HCF}$ and $\mathrm{LCM}$ of $37$ and $49$ by prime factorisation method.

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

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

Express $3825$ as a product of its prime factors.