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  1. 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
  2. Euclidean algorithm - Wikipedia
    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 ...
    en.wikipedia.org/wiki/Euclidean_algorithm
  3. The Euclidean Algorithm (article) | Khan Academy
    Read and learn for free about the following article: The Euclidean Algorithm.
    www.khanacademy.org/.../a/the-euclidean-algorithm
  4. Euclidean Algorithm -- from Wolfram MathWorld
    For 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
  5. Euclidean algorithm - Rutgers Math Department
    Formal 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
  6. The Euclidean Algorithm - YouTube
    Top comments; Newest first. Dimitris Kapsis1 year ago. Wtf is this video? it doesnt work like ...
    www.youtube.com/watch?v=p5gn2hj51hs
  7. The Euclidean Algorithm (GCD or GCF) - YouTube
    Here is the Euclidean Algorithm! A great way to find the gcf/gcd of two numbers. Thank you, Euclid.
    www.youtube.com/watch?v=AJn843kplDw
  8. 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
  9. 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
  10. 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
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