A number which can be expressed in the form of $\frac{p}{q}, q \neq 0$ and $p, q \in \mathrm{Z}$, is called a rational number. Its decimal representation is either terminating or non-terminating repeating.

A number which cannot be expressed in the form of $\frac{p}{q}, q \neq 0$ and $p, q \in \mathrm{Z}$, is called a irrational number. Its decimal representation is non-terminating o non-repeating repeating.

Every composite number can be factorised as a product of primes and its factorisation is unique, apart from the order in which the prime occur.

If p is a prime and p divides a², then p divides a, where a is a positive integer.

For any two positive integers $p$ and $q$, we have
HCF $(p, q) \times \operatorname{LCM}[p, q]=p \times q$ $$ \begin{aligned} \operatorname{HCF}(p, q) &=\frac{p \times q}{\operatorname{LCM}[p, q]} \\ \operatorname{LCM}[p, q] &=\frac{p \times q}{\operatorname{HCF}(p, q)} \end{aligned} $$

For any three positive integers $p, q$ and $r$, we have $$ \begin{aligned} &\operatorname{HCF}(p, q, r)=\frac{p \times q \times r \times \operatorname{LCM}[p, q, r]}{\operatorname{LCM}[p, q] \times \operatorname{LCM}[q, r] \times \operatorname{LCM}[r, p]} \\ &\operatorname{LCM}[p, q, r]=\frac{p \times q \times r \times \operatorname{HCF}(p, q, r)}{\operatorname{HCF}(p, q) \times \operatorname{HCF}(q, r) \times \operatorname{HCF}(r, p)} \end{aligned} $$