- ユークリッドの互除法 - Wikipediaユークリッドの互除法（ユークリッドのごじょほう、英:
**Euclidean Algorithm**）は、2 つの 自然数の最大公約数を求める手法の一つである。 2 つの自然数 a, b (a ≧ b) について 、a の b による剰余を r とすると、 a と b との最大公約数は b と r との最大公約数に 等しいという性質が成り立つ。この性質を利用して、 b を r で割った剰余、 除数 r をその 剰余で割った剰余、と剰余を求める計算を逐次繰り返すと、剰余が 0 になった時の除数 が a と b との最大公約数となる。 明示的に記述された最古のアルゴリズムとしても知 られ、 ...*ja.wikipedia.org/wiki/ユークリッドの互除法* **Euclidean algorithm**- WikipediaIn 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 ...*en.wikipedia.org/wiki/***Euclidean**_**algorithm**- The
**Euclidean Algorithm**(article) | Khan AcademyRead and learn for free about the following article: The**Euclidean Algorithm**.*www.khanacademy.org/.../a/the-***euclidean**-**algorithm** **Euclidean Algorithm**-- from Wolfram MathWorldFor integers, the algorithm terminates when q_(n+1) divides r_(n-1) exactly, at which point r_n corresponds to the greatest common divisor of a and b , GCD(a,b )=r_n . For real numbers, the algorithm yields either an exact relation or an infinite sequence of approximate relations (Ferguson et al. 1999). An important consequence of the**Euclidean algorithm**is finding integers x and y such that ...*mathworld.wolfram.com > ... > Greatest Common Divisor***Euclidean algorithm**- Rutgers Math DepartmentFormal description of the**Euclidean algorithm**. Input Two positive integers, a and b. Output The greatest common divisor, g, of a and b. Internal computation. If a<b, exchange a and b. Divide a by b and get the remainder, r. If r=0, report b as the GCD of a and b. Replace a by b and replace b by r. Return to the previous step.*www.math.rutgers.edu/~greenfie/gs2004/***euclid**.html- The
**Euclidean Algorithm**- YouTubeTop comments; Newest first. Dimitris Kapsis1 year ago. Wtf is this video? it doesnt work like**...***www.youtube.com/watch?v=p5gn2hj51hs* - The
**Euclidean Algorithm**(GCD or GCF) - YouTubeHere is the**Euclidean Algorithm**! A great way to find the gcf/gcd of two numbers. Thank you, Euclid.*www.youtube.com/watch?v=AJn843kplDw* - Number Theory -
**Euclid's Algorithm**The obvious answer is to list all the divisors a and b , and look for the greatest one they have in common. However, this requires a and b to be factorized, and it is not known how we can do this efficiently. Amazingly, a few simple observations lead to a far superior method:**Euclid's algorithm**(also known as the**Euclidean****algorithm**). First, if d divides a and d divides b , then d divides their sum. Similarly, d must also divide their difference, a - b , where a is the larger of the two. But this ...*crypto.stanford.edu/pbc/notes/.../***euclid**.html - 3.3 The
**Euclidean Algorithm**It perhaps is surprising to find out that this lemma is all that is necessary to compute a gcd, and moreover, to compute it very efficiently. This remarkable fact is known as the**Euclidean Algorithm**. As the name implies, the**Euclidean****Algorithm**was known to Euclid, and appears in The Elements; see section 2.6. As we will see, the**Euclidean Algorithm**is an important theoretical tool as well as a practical algorithm. Here is how it works: To compute ( a , b ) , divide the larger number (say a ) ...*www.whitman.edu/mathematics/.../section03.03.html* **Euclid's Algorithm**- Interactive Mathematics Miscellany and Puzzles**Euclid's Algorithm**appears as the solution to the Proposition VII.2 in the Element's: Given two numbers not prime to one another, to find their greatest common measure.*www.cut-the-knot.org/blue/***Euclid**.shtml