# Euclidean algorithm - Flowchart

"In mathematics, the Euclidean algorithm, or Euclid's algorithm, is a method for computing the greatest common divisor (GCD) of two (usually positive) integers, also known as the greatest common factor (GCF) or highest common factor (HCF). ...

The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in general is defined in a more subtle way).

In its simplest form, Euclid's algorithm starts with a pair of positive integers, and forms a new pair that consists of the smaller number and the difference between the larger and smaller numbers. The process repeats until the numbers in the pair are equal. That number then is the greatest common divisor of the original pair of integers.

The main principle is that the GCD does not change if the smaller number is subtracted from the larger number. ... Since the larger of the two numbers is reduced, repeating this process gives successively smaller numbers, so this repetition will necessarily stop sooner or later - when the numbers are equal (if the process is attempted once more, one of the numbers will become 0)." [Euclidean algorithm. Wikipedia]

The flowchart example "Euclidean algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park. Read more

The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in general is defined in a more subtle way).

In its simplest form, Euclid's algorithm starts with a pair of positive integers, and forms a new pair that consists of the smaller number and the difference between the larger and smaller numbers. The process repeats until the numbers in the pair are equal. That number then is the greatest common divisor of the original pair of integers.

The main principle is that the GCD does not change if the smaller number is subtracted from the larger number. ... Since the larger of the two numbers is reduced, repeating this process gives successively smaller numbers, so this repetition will necessarily stop sooner or later - when the numbers are equal (if the process is attempted once more, one of the numbers will become 0)." [Euclidean algorithm. Wikipedia]

The flowchart example "Euclidean algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park. Read more

## Basic Flowchart Symbols and Meaning

Flowcharts are the best for visually representation the business processes and the flow of a custom-order process through various departments within an organization. ConceptDraw PRO diagramming and vector drawing software extended with Flowcharts solution offers the full set of predesigned basic flowchart symbols which are gathered at two libraries: Flowchart and Flowcharts Rapid Draw. Among them are: process, terminator, decision, data, document, display, manual loop, and many other specific symbols. The meaning for each symbol offered by ConceptDraw gives the presentation about their proposed use in professional Flowcharts for business and technical processes, software algorithms, well-developed structures of web sites, Workflow diagrams, Process flow diagram and correlation in developing on-line instructional projects or business process system. Use of ready flow chart symbols in diagrams is incredibly useful - you need simply drag desired from the libraries to your document and arrange them in required order. There are a few serious alternatives to Visio for Mac, one of them is ConceptDraw PRO. It is one of the main contender with the most similar features and capabilities. Read more## Mathematics

Mathematics solution extends ConceptDraw PRO software with templates, samples and libraries of vector stencils for drawing the mathematical illustrations, diagrams and charts. Read more

"In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form

ax^2+bx+c=0

where x represents an unknown, and a, b, and c are constants with a not equal to 0. If a = 0, then the equation is linear, not quadratic. The constants a, b, and c are called, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.

Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using the quadratic formula, or by graphing." [Quadratic equation. Wikipedia]

The flowchart example "Solving quadratic equation algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park. Read more

ax^2+bx+c=0

where x represents an unknown, and a, b, and c are constants with a not equal to 0. If a = 0, then the equation is linear, not quadratic. The constants a, b, and c are called, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.

Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using the quadratic formula, or by graphing." [Quadratic equation. Wikipedia]

The flowchart example "Solving quadratic equation algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park. Read more

## Basic Diagramming

Mathematics is an exact science, which studies the values, spatial forms and quantitative relations. It is a science, in which is built large number of various diagrams, charts and graphs that present the material in a clear, visual and colorful form, help to analyze the information and to make certain conclusions. A diagram is a graphical representation of data using the linear segments or geometric shapes, which allows to evaluate the ratio of several values. Depending on the types of solved tasks are used the diagrams of different kinds. A graph is a diagram that shows quantitative dependencies of various processes using the curves. ConceptDraw PRO is a powerful intelligent and multifunctional vector engine for drawing different Mathematical diagrams and graphs, Mathematical illustrations, complex and simple Diagram mathematics, Flowcharts of equation solving process, Line graphs, Scatter plots, Histograms, Block diagrams, Bar charts, Divided bar diagrams, Pie charts, Area charts, Circular arrows diagrams, Venn diagrams, Bubble diagrams, Concept maps, and many others. Read more## Types of Flowcharts

A Flowchart is a graphical representation of process, algorithm, workflow or step-by-step solution of the problem. It shows the steps as boxes of various kinds and connects them by arrows in a defined order depicting a flow. There are twelve main Flowchart types: Basic Flowchart, Business Process Modeling Diagram (BPMN), Cross Functional Flowchart, Data Flow Diagram (DFD), IDEF (Integrated DEFinition) Flowchart, Event-driven Process Chain (EPC) Diagram, Influence Diagram (ID), Swimlane Flowchart, Process Flow Diagram (PFD), Specification and Description Language (SDL) Diagram, Value Stream Mapping, Workflow Diagram. Using the Flowcharts solution from the Diagrams area of ConceptDraw Solution Park you can easy and quickly design a Flowchart of any of these types. This solution offers a lot of special predesigned vector symbols for each of these widely used notations. They will make the drawing process of Flowcharts much easier than ever. Pay also attention for the included collection of ready Flowchart examples, samples and quick-start templates. This is business process improvement tools. If you are looking for MS Visio for your Mac, then you are out of luck, because it hasn't been released yet. However, you can use Visio alternatives that can successfully replace its functions. ConceptDraw PRO is an alternative to MS Visio for Mac that provides powerful features and intuitive user interface for the same. Read more## Process Flowchart

The main reason of using Process Flowchart or PFD is to show relations between major parts of the system. Process Flowcharts are used in process engineering and chemical industry where there is a requirement of depicting relationships between major components only and not include minor parts. Process Flowcharts for single unit or multiple units differ in their structure and implementation. ConceptDraw PRO is Professional business process mapping software for making Process flowcharts, Process flow diagram, Workflow diagram, flowcharts and technical illustrations for business documents and also comprehensive visio for mac application. Easier define and document basic work and data flows, financial, production and quality management processes to increase efficiency of your business with ConcepDraw PRO. Business process mapping software with Flowchart Maker ConceptDraw PRO includes extensive drawing tools, rich examples and templates, process flowchart symbols and shape libraries, smart connectors that allow you create the flowcharts of complex processes, process flow diagrams, procedures and information exchange. Process Flowchart Solution is project management workflow tools which is part ConceptDraw Project marketing project management software. Drawing charts, diagrams, and network layouts has long been the monopoly of Microsoft Visio, making Mac users to struggle when needing such visio alternative like visio for mac, it requires only to view features, make a minor edit to, or print a diagram or chart. Thankfully to MS Visio alternative like ConceptDraw PRO software, this is cross-platform charting and business process management tool, now visio alternative for making sort of visio diagram is not a problem anymore however many people still name it business process visio tools. Read more## Flowcharts

The Flowcharts solution for ConceptDraw PRO is a comprehensive set of examples and samples in several varied color themes for professionals that need to represent graphically a process. Solution value is added by the basic flow chart template and shapes' libraries of flowchart notation. ConceptDraw PRO flow chart creator lets one depict the processes of any complexity and length, as well as design the Flowchart either vertically or horizontally. Read more

## Simple Flow Chart

ConceptDraw PRO diagramming and vector drawing software extended with Flowcharts Solution from the 'Diagrams' area of ConceptDraw Solution Park is a powerful tool for drawing Flow Charts of any complexity you need. Irrespective of whether you want to draw a Simple Flow Chart or large complex Flow Diagram, you estimate to do it without efforts thanks to the extensive drawing tools of Flowcharts solution, there are professional flowchart symbols and basic flowchart symbols. This sample shows the Gravitational Search Algorithm (GSA) that is the optimization algorithm. Read more## Types of Flowchart - Overview

When designing a process or an instruction in clear and understandable way, you should consider creating a flowchart. You can avoid spending a lot of time understanding complex concepts as they get clear with different diagrams. The flowcharts are very popular diagram type, they are useful at different fields from the description business processes to the presentation of cooking recipes. Basic Flowchart, Business Process Modeling Diagram, Process Flowchart, Cross Functional Flowchart, Procedure Flowchart, Data Flow Diagram, IDEF Flowchart, SDL Diagram, Workflow Diagram, Document Flowchart, Program Flowchart, Value Stream Map, System Flowchart, Highlight Flowchart, Sales Flowchart are the main types flowchart. The ConceptDraw PRO is one of the professional applications which has great advantages and using which you can create different types of Flowcharts easy and fast. Try to draw an illustrative and comprehensible diagram in ConceptDraw PRO describing the processes instead of writing complex long text and make sure how it is convenient. Visio is expensive, and if you use it in a team environment, these costs are compounded. ConceptDraw PRO is an affordable alternative to Visio and luckily, it comes with a team plan. ConceptDraw PRO can import and export Visio files, so Mac users can collaborate with PC users stuck on Microsoft's software. Read more## Basic Diagramming

Create flowcharts, flow charts, and more with ConceptDraw flowchart software. Read more## Horizontal Flowchart

This sample was created in ConceptDraw PRO diagramming and vector drawing software using the Flowcharts solution from the Diagrams area of ConceptDraw Solution Park. A Flowchart is a graphically representation of the process, algorithm or the step-by-step solution of the problem. The Flowcharts have one or more starting and ending points. The geometric figures on the Flowcharts represent the steps of the process and are connected with arrows that show the sequence of the actions. Read more## Flow Chart Symbols

ConceptDraw PRO software extended with Flowcharts Solution from the "Diagrams" Area is a powerful software that will help you design the flowcharts for any business and technical processes, and software algorithms thanks to the predesigned flow chart symbols. Flowcharts solution offers 2 libraries with large collection of vector flow chart symbols: Flowchart Library, Flowcharts Rapid Draw Library that you can use to create your flowcharts quick and easy. Flowchart Solution is number of diagraming stencils including special set of flow chart symbols such as: terminator, process, decision which indicates a decision points between two or more paths in a flowchart, symbol of delay. Major symbols includes symbol of data, document or multiple documents, subroutine, preparation for processing of documents. Also includes symbols: display, manual input, manual loop, loop limit, stored data,connectors and suming junctions, sort and merge operations, symbols of database and internal stor Read more## Simple Drawing Applications for Mac

ConceptDraw gives the ability to draw simple diagrams like flowcharts, block diagrams, bar charts, histograms, pie charts, divided bar diagrams, line graphs, area charts, scatter plots, circular arrows diagrams, Venn diagrams, bubble diagrams, concept maps, and others. Read more- Mathematical Example Of Algorithm And Flowchart
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