Euclids Extended Algorithm 2 and 17

Using Euclids Extended Algorithm: Calculate x and y in Bzout's Identity using (2,17) For 2 numbers a and b and divisor d: ax + by = d a = -8 and b = 1 ax + by = gcd(a,b) 2x + 17y = gcd(2 GCF(2, 17) = 1

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Using Euclids Extended Algorithm:

Calculate x and y in Bézout's Identity

using (2,17)

Bezouts Identity

For 2 numbers a and b and divisor d:

ax + by = d

Extended Algorithm Table
a mathab mathbd mathdk mathk
Set to 11Set to 002
Set to 00Set to 1117Quotient of 2/170
1 - (0 x 0)10 - (0 x 1)0Remainder of 2/172Quotient of 17/28
0 - (8 x 1)-81 - (8 x 0)1Remainder of 17/21Quotient of 2/12
1 - (2 x -8)170 - (2 x 1)-2Remainder of 2/10Quotient of 1/00

Take the last non-zero row for d:

a = -8 and b = 1

GCD Equation

ax + by = gcd(a,b)

2x + 17y = gcd(2

GCF(2, 17) = 1

Final Answer:

GCF(2, 17) = 1

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What is the Answer?

GCF(2, 17) = 1

How does the Euclids Algorithm and Euclids Extended Algorithm Calculator work?

Free Euclids Algorithm and Euclids Extended Algorithm Calculator - Given 2 numbers a and b, this calculates the following
1) The Greatest Common Divisor (GCD) using Euclids Algorithm
2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm Extended Euclidean Algorithm
This calculator has 2 inputs.

What 1 formula is used for the Euclids Algorithm and Euclids Extended Algorithm Calculator?

What 8 concepts are covered in the Euclids Algorithm and Euclids Extended Algorithm Calculator?

algorithmA process to solve a problem in a set amount of timeequationa statement declaring two mathematical expressions are equaleuclids algorithmmethod for computing the greatest common divisor (GCD) of two numberseuclids extended algorithmdivision algorithm for integersgreatest common factorlargest positive integer dividing a set of integersidentityan equality that holds true regardless of the values chosen for its variablesquotientThe result of dividing two expressions.remainderThe portion of a division operation leftover after dividing two integers

Example calculations for the Euclids Algorithm and Euclids Extended Algorithm Calculator

Euclids Algorithm and Euclids Extended Algorithm Calculator Video


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