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

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

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

Find the $LCM$ and $HCF$ of the following pairs of integers and verify that $LCM \times HCF =$ product of the two numbers $26$ and $91$.

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 $5-\sqrt{3}$ is irrational.