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Use the Euclidean algorithm to finda) gcd(1,

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 32E Chapter 4.3

Discrete Mathematics and Its Applications | 7th Edition

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

Discrete Mathematics and Its Applications | 7th Edition

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Problem 32E

Use the Euclidean algorithm to find

a) gcd(1, 5).

b) gcd(100,101).

c) gcd(123,  277).

d) gcd(1529, 14039).

e) gcd( 1529, 14038).

f) gcd( 11111, 111111).

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

We have to use the Euclidean algorithm to find gcd.

Step2

a) gcd(1, 5)

By using  Euclidean algorithm

As 1 is the last nonzero remainder.

Therefore,  gcd(1, 5) is 1.

Step3

b) gcd(100,101)

By using  Euclidean algorithm

As 1 is the last nonzero remainder.

Therefore,  gcd(100, 101) is 1.

Step4

c) gcd(123,  277)

By using  Euclidean algorithm

As 1 is the last nonzero remainder.

Therefore,   gcd(123,  277) is 1.

Step5

d) gcd(1529, 14039)

By using  Euclidean algorithm

Step 2 of 3

Chapter 4.3, Problem 32E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Use the Euclidean algorithm to finda) gcd(1,

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