Use the extended Euclidean algorithm to express gcd( 144,

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

ISBN: 9780073383095 37

Solution for problem 43E Chapter 4.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 43E

Use the extended Euclidean algorithm to express gcd( 144, 89) as a linear combination of 144 and 89.

Step-by-Step Solution:

Solution :

Step 1 :

In this problem we have to express the gcd as a linear combination.

Given numbers are 144 and 89.

The Euclidean algorithm uses these divisions.

$144=1.89+55..............(1)$

$89=1.55+34................(2)$

$55=1.34+21................(3)$

$34=1.21+13................(4)$

$21=1.13+8..................(5)$

$13=1.8+5....................(6)$

$8=1.5+3......................(7)$

$5=1.3+2......................(8)$

$3=1.2+1.....................(9)$

$2=2.1..........................(10)$

$.'.\ gcd(144,89)=1$

Step 2 of 3

Chapter 4.3, Problem 43E is Solved

Step 3 of 3

Textbook: Discrete Mathematics and Its Applications

Edition: 7

Author: Kenneth Rosen

ISBN: 9780073383095

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