In mathematics and computer science, an **algorithm** is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks.

A graphical expression of Euclid’s algorithm to find the greatest common divisor for 1599 and 650.

```
1599 = 650×2 + 299
650 = 299×2 + 52
299 = 52×5 + 39
52 = 39×1 + 13
39 = 13×3 + 0
```

An algorithm is an effective method that can be expressed within a finite amount of space and time^{} and in a well-defined formal language^{} for calculating a function.^{} Starting from an initial state and initial input (perhaps empty),^{} the instructions describe a computation that, when executed, proceeds through a finite^{} number of well-defined successive states, eventually producing “output”^{} and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.^{}

What is Euclid ‘s Algorithm ?

Euclid ‘s algorithm to compute the greatest common divisor (GCD) to two numbers appears as Proposition II in Book VII (“Elementary Number Theory”) of his *Elements*.^{} Euclid poses the problem thus: “Given two numbers not prime to one another, to find their greatest common measure”. He defines “A number [to be] a multitude composed of units”: a counting number, a positive integer not including zero. To “measure” is to place a shorter measuring length *s* successively (*q* times) along longer length *l* until the remaining portion *r* is less than the shorter length *s*.

How to solve Euclid ‘s Algorithm ?

GOOD TRY.