- published: 17 Dec 2012
- views: 175695
GCD may refer to:
In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.
The greatest common divisor is also known as the greatest common factor (gcf),highest common factor (hcf),greatest common measure (gcm), or highest common divisor.
This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below).
In this article we will denote the greatest common divisor of two integers a and b as gcd(a,b).
Some textbooks use (a,b).
The J programming language uses a +. b
The number 54 can be expressed as a product of two integers in several different ways:
Thus the divisors of 54 are:
Similarly, the divisors of 24 are:
The numbers that these two lists share in common are the common divisors of 54 and 24:
The greatest of these is 6. That is, the greatest common divisor of 54 and 24. One writes:
Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.
The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.
In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in Euclid's Elements (c. 300 BC). It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations.
The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 147 = 252 − 105. Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until one of the two numbers reaches zero. When that occurs, the other number (the one that is not zero) is the GCD of the original two numbers. By reversing the steps, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e.g., 21 = 5 × 105 + (−2) × 252. The fact that the GCD can always be expressed in this way is known as Bézout's identity.
Common may refer to:
This tutorial demonstrates how the euclidian algorithm can be used to find the greatest common denominator of two large numbers. Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm Donate http://bit.ly/19AHMvX
Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc We talk about prime numbers and the greatest common denominator of two numbers. We do a proof that shows that the set of primes is infinite. Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
Here is the Euclidean Algorithm! A great way to find the gcf/gcd of two numbers. Thank you, Euclid.
Introduction to Highest Common Factor or Greatest Common Divisor. In short it is also referred as HCF or GCD. For more videos on this topic and many more interesting topic visit or subscribe to : https://www.youtube.com/MathsSmart
In this video we will learn to find GCD or Greatest Common Divisor using recursion. You can download the project code from my GitHub repository https://github.com/yusufshakeel/C-Project
This tutorial on datapaths and state machines for computing the GCD accompanies the book Digital Design Using Digilent FPGA Boards - VHDL / Active-HDL Edition which contains over 75 examples that show you how to design digital circuits using VHDL, simulate them using the Aldec Active-HDL simulator, and synthesize the designs to a Xilinx FPGA. Visit www.lbebooks.com for more information or to purchase this inexpensive, informative, award winning book.
The greatest common divisor is defined and the Euclidean Algorithm is used to calculate the gcd.
The solution to a typical GCD exam question. See my other videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.
Learn how to find the Greatest Common Divisor (GCD) with this cool, easy, simple and free math guide!. This math guide use the factors descomposition method using the prime numbers (a fast method)!. NOTE: This guide maybe is hard for kids in elementary school!. If you need help knowing what are prime numbers, search on Google. The only thing you need to do these exercises is to know the prime numbers. Like! Comment! Subscribe! Share! Share Everywhere! Visit LearnMathStd Website for non-videos tutorials: http://learnmathstd.tk Thank you for watching, Keep sharing!. Christian Carrion - LearnMathStd
Here's a nice explanation of least common factor (or least common divisor) along with a few practice example exercises. Let's roll. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/factors-multiples/greatest_common_divisor/e/greatest_common_divisor?utm_source=YT&utm;_medium=Desc&utm;_campaign=PreAlgebra Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/factors-multiples/greatest_common_divisor/v/lcm-and-gcf-greatest-common-factor-word-problems?utm_source=YT&utm;_medium=Desc&utm;_campaign=PreAlgebra Missed the previous lesson? https://www.khanacademy.org/math/pre-algebra/factors-multiples/greatest_common_divisor/v/greatest-common-divisor-factor-exercise?utm_source=YT&utm;_medium=Desc&utm;_campaign=PreAlgebra Pre-Algebr...
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In this video we use the Euclidean Algorithm to find the gcd of two numbers, then use that process in reverse to write the gcd as a linear combination of the two numbers.
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