   Chapter 8.4, Problem 26ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 26 and 27, use the extended Euclidean algorithm to find the greatest common divisor of the given numbers and express it as a linear combination of the two numbers. 6664 and 765

To determine

To calculate:

The greatest common divisor of 6664and765 and express it in a linear combination of two numbers.

Explanation

Given information:

The given numbers are 6664and765.

Formula used:

Division algorithm:

Let a be an integer and d be a positive integer. Then, there are unique integers qandr with 0r<d such that a=dq+r, here, q is the quotient and r is the remainder.

The greatest common divisor of two numbers aandb is the integer d which satisfies the following properties:

d|aandd|b

For all integers c, when c|aandc|b, then cd.

Calculation:

To find the greatest common divisor, use the Euclidean algorithm.

Step 1: 6664=765×8+544544=6664765×8

Step 2: 765=544×1+221221=765544×1

Step 3: 544=221×2+102102=544221×2

Step 4: 221=102×2+1717=221102×2

Step 5: 102=17×6+0

So, 17 is the remainder

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