What is an algorithm?

Algorithm is a step-by-step procedure for calculations.

For example:

Euclid's Division Algorithm: In order to compute the HCF of two positive integers say $a$ and $b$, with $a>b$ by using Euclid's algorithm, we follow the following steps:

$\underline{\text { STEP I }}$ : Apply Euclid's Division Lemma to $a$ and $b$ and obtain whole numbers $q_{1}$ and $r_{1}$, such that $a=b q_{1}+r_{1}, 0 \leq r_{1}

$\underline{\text { STEP II: If }} r_{1}=0, b$ is the HCF of $a$ and $b$.

STEP III: If $r_{1} \neq 0$, apply Euclid's division lemma to $b$ and $r_{1}$ and obtain whole numbers $q_{1}$ and $r_{2}$, such that $b=q_{1} r_{1}+r_{2}$

STEP IV: If $r_{2}=0$, then $r_{1}$ is the HCF of $a$ and $b$.

$\underline{\text { STEP V: }}$ If $r_{2} \neq 0$, then apply Euclid's division lemma to $r_{1}$ and $r_{2}$ and continue the above process till the remainder $r_{n}$ is zero. The divisor at this stage i.e; $r_{n-1}$, or the non-zero remainder at the previous stage is the HCF of $a$ and $b$.