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.

"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.

This opportunity flowchart sample shows the steps involved in replacing engine oil process. The opportunity flowcharts are used in business process improvement to identify process steps which might be improved.
"Business process improvement (BPI) is a systematic approach to help an organization optimize its underlying processes to achieve more efficient results. ...
An organization is only as good as its processes. To be able to make the necessary changes in an organization, one needs to understand the key processes of the company. Rummler and Brache suggested a model for running a Process Improvement and Management project (PI&M), containing the following steps:
1. Identify the process to be improved (based on a critical business issue): The identification of key processes can be a formal or informal exercise. The management team might select processes by applying a set of criteria derived from strategic and tactical priorities, or process selection is based on obvious performance gaps. It is important is to select the process(es) which have the greatest impact on a competitive advantage or customer requirement.
2. Develop the objective(s) for the project based on the requirements of the process: The focus might be on quality improvement, productivity, cost, customer service or cycle time. The goal is however always the same; to get the key process under control.
3. Select the members of the cross-functional team: A horizontal (cross-functional) analysis is carried out by a team composed of representatives of all functions involved in the process. While a consultant or in-house staff person can do the job, the quality of the analysis and the commitment to change is far greater with a cross-functional team.
4. Document the current process by creating a flowchart or "organization map": Describe the process regarding the Organizational level, the Process level and the Job/ Performer level according to Rummler. Develop a cross-functional process map for the process.
5. Identify "disconnects" in the process: “Disconnections” are everything that inhibit the efficiency and effectiveness of the process. The identification should be categorized into the three levels: The Organizational level, the Process level and the Job/ Performer level.
6. Recommend changes (organizational, in the process or in its execution): Categorize and prioritize the main problems and possibilities, evaluate alternative solutions. Develop a cross-functional process map for the recommended process.
7. Establish process and sub-process measures: The process measures should reflect the objectives of the project.
8. Implement the improvements." [Business process improvement. Wikipedia]
The swim lane diagram example "Opportunity flowchart - Replacing engine oil" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Cross-Functional Flowcharts solution from the Business Processes area of ConceptDraw Solution Park.