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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.3 - Problem 24e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.3 - Problem 24e

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# What are the greatest common divisors of these pairs of ISBN: 9780073383095 37

## Solution for problem 24E Chapter 4.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 24E

What are the greatest common divisors of these pairs of integers?a) 22 · 33 · 55 , 25 · 33 · 52________________b) 2·3·5·7 · 11 ·13 , 211 ·39· 11 ·1714________________c) 17, 1717________________d) 22 · 7, 53 · 13________________e) 0, 5________________f) 2·3·5·7, 2·3·5·7

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Solution:-Step1Given thatWe have to find what are the greatest common divisors of these pairs of integersStep2a) 22 · 33 · 55, 25 · 33 · 52Definition: - The greatest common divisor, sometimes also called the highest common divisor of two positive integers c and d are the largest divisor common to c and d.The positive common divisor of two number isSo, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are .Step3b) 2·3·5·7 · 11 ·13 , 211 ·39· 11 ·1714The positive common divisor of two number isSo, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are .Step4c) 17, 1717The positive common divisor of two number isSo, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are 17.Step5d) 22 · 7, 53 · 13The positive common divisor of two number is 1So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are 1.Step6e) 0, 5The positive common divisor of two number is 5So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are 5.Step7f) 2·3·5·7, 2·3·5·7The positive common divisor of two number is So, gcd (gcd=greatest common divisors)Therefore, the greatest common divisors of these pairs of integers are .

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##### ISBN: 9780073383095

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