1.1 / May 2, 2016
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Description

The Euclidean algorithm is usually usedsimplyto find the greatest common divisor of two integers. (Foradescription of this algorithm, see the notes aboutadditionaltopics in number theory.) The standard Euclideanalgorithm givesthe greatest common divisor and nothing else.However, if we keeptrack of a bit more information as we go throughthe algorithm, wecan discover how to write the greatest commondivisor as an integerlinear combination of the two originalnumbers. In other words, wecan find integers s and t such that

gcd(a, b) = sa + tb.

[Note that, since gcd(a, b) is usually less than both a andb,one of s or t will usually be negative.]

As a reminder, here are the steps of the standardEuclideanalgorithm to find the greatest common divisor of twopositiveintegers a and b:

Set the value of the variable c to the larger of the two valuesaand b, and set d to the smaller of a and b.
Find the remainder when c is divided by d. Call thisremainderr.
If r = 0, then gcd(a, b) = d. Stop.
Otherwise, use the current values of d and r as the new values ofcand d, respectively, and go back to step 2.
The extended Euclidean algorithm uses the same framework, butthereis a bit more bookkeeping. Before we present a formaldescriptionof the extended Euclidean algorithm, let’s work our waythrough anexample to illustrate the main ideas.

App Information Extended Euclidean Algorithm

  • App Name
    Extended Euclidean Algorithm
  • Package Name
    com.gokhankurt.extendedeuclid
  • Updated
    May 2, 2016
  • File Size
    Undefined
  • Requires Android
    Android 4.2 and up
  • Version
    1.1
  • Developer
    gokhanku
  • Installs
    10 - 50
  • Price
    Free
  • Category
    Education
  • Developer
  • Google Play Link

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Extended Euclidean Algorithm 1.1 APK
gokhanku
The Euclidean algorithm is usually usedsimplyto find the greatest common divisor of two integers. (Foradescription of this algorithm, see the notes aboutadditionaltopics in number theory.) The standard Euclideanalgorithm givesthe greatest common divisor and nothing else.However, if we keeptrack of a bit more information as we go throughthe algorithm, wecan discover how to write the greatest commondivisor as an integerlinear combination of the two originalnumbers. In other words, wecan find integers s and t such thatgcd(a, b) = sa + tb.[Note that, since gcd(a, b) is usually less than both a andb,one of s or t will usually be negative.]As a reminder, here are the steps of the standardEuclideanalgorithm to find the greatest common divisor of twopositiveintegers a and b:Set the value of the variable c to the larger of the two valuesaand b, and set d to the smaller of a and b.Find the remainder when c is divided by d. Call thisremainderr.If r = 0, then gcd(a, b) = d. Stop.Otherwise, use the current values of d and r as the new values ofcand d, respectively, and go back to step 2.The extended Euclidean algorithm uses the same framework, butthereis a bit more bookkeeping. Before we present a formaldescriptionof the extended Euclidean algorithm, let’s work our waythrough anexample to illustrate the main ideas.