Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 4 - Section 4.3 - Primes and Greatest Common Divisors - Exercises - Page 273: 25

Answer

a. 3^{5} \times 5^(3) b. 1 c. 23^(17) d. 41 \times 43 \ times 53 e. 1 f. 1111

Work Step by Step

Let a^(n) be an integer, then a is called a basis and n is called a degree. To solve greatest common divisor between two number, then find the least degree if there are same basis of two numbers. a. the least degree between basis of 3 is 5 and basis of 5 is 3. b. there are no same basis between those number so the answer is 1 c. the least degree between two numbers with basis of 23 is 17 d. the least degree between same basis is 41, 43, and 53 e. there are no same basis between those number so the answer is 1 f. the greatest common divisor between a non-zero number and 0 is the non-zero number itself
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