Mathematical Excursions (MindTap Course List)
Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…
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Chapter 6.5, Problem 73ES

Number of Divisors of a Composite Number The following method can be used to determine the number of divisors of a composite number. First find the prime factorization (in exponential form) of the composite number. Add 1 to each exponent in the prime factorization and then compute the product of these exponents. This product is equal to the number of divisors of the composite number. To illustrate that this procedure yields the correct result, consider the composite number 12, which has the six divisors 1, 2, 3, 4, 6, and 12. The prime factorization of 12 is 2 2 ⋅ 3 1 . Adding 1 to each of the exponents produces the numbers 3 and 2. The product of 3 and 2 is 6, which agrees with the result obtained by listing all of the divisors.

Determine the number of divisors of each composite number.

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Chapter 6 Solutions

Mathematical Excursions (MindTap Course List)

Ch. 6.1 - Complete the crossword puzzle shown on the...Ch. 6.1 - Prob. 2EECh. 6.1 - Write 357 as a traditional Chinese numeral.Ch. 6.1 - Prob. 4EECh. 6.1 - Prob. 5EECh. 6.1 - Prob. 6EECh. 6.1 - Prob. 1ESCh. 6.1 - Prob. 2ESCh. 6.1 - Prob. 3ESCh. 6.1 - Prob. 4ES
Ch. 6.1 - Prob. 5ESCh. 6.1 - Prob. 6ESCh. 6.1 - Prob. 7ESCh. 6.1 - Write each Hindu-Arabic numeral using Egyptian...Ch. 6.1 - Prob. 9ESCh. 6.1 - Prob. 10ESCh. 6.1 - Prob. 11ESCh. 6.1 - Prob. 12ESCh. 6.1 - Prob. 13ESCh. 6.1 - Prob. 14ESCh. 6.1 - Prob. 15ESCh. 6.1 - Write each Egyptian numeral as a Hindu-Arabic...Ch. 6.1 - Prob. 17ESCh. 6.1 - Prob. 18ESCh. 6.1 - Prob. 19ESCh. 6.1 - Prob. 20ESCh. 6.1 - Prob. 21ESCh. 6.1 - Prob. 22ESCh. 6.1 - Prob. 23ESCh. 6.1 - Prob. 24ESCh. 6.1 - Prob. 25ESCh. 6.1 - Prob. 26ESCh. 6.1 - Prob. 27ESCh. 6.1 - Prob. 28ESCh. 6.1 - Use Egyptian hieroglyphics to find each sum or...Ch. 6.1 - Use Egyptian hieroglyphics to find each sum or...Ch. 6.1 - Use Egyptian hieroglyphics to find each sum or...Ch. 6.1 - Prob. 32ESCh. 6.1 - Prob. 33ESCh. 6.1 - Write each Roman numeral as a Hindu-Arabic...Ch. 6.1 - Prob. 35ESCh. 6.1 - Prob. 36ESCh. 6.1 - Prob. 37ESCh. 6.1 - Prob. 38ESCh. 6.1 - Prob. 39ESCh. 6.1 - Prob. 40ESCh. 6.1 - Prob. 41ESCh. 6.1 - Prob. 42ESCh. 6.1 - Prob. 43ESCh. 6.1 - Prob. 44ESCh. 6.1 - Prob. 45ESCh. 6.1 - Prob. 46ESCh. 6.1 - Prob. 47ESCh. 6.1 - Prob. 48ESCh. 6.1 - Prob. 49ESCh. 6.1 - Prob. 50ESCh. 6.1 - Prob. 51ESCh. 6.1 - Prob. 52ESCh. 6.1 - Prob. 53ESCh. 6.1 - Prob. 54ESCh. 6.1 - Prob. 55ESCh. 6.1 - Prob. 56ESCh. 6.1 - Prob. 57ESCh. 6.1 - Prob. 58ESCh. 6.1 - Prob. 59ESCh. 6.1 - Prob. 60ESCh. 6.1 - Egyptian Multiplication TheRhind papyrus contains...Ch. 6.1 - Egyptian Multiplication TheRhind papyrus contains...Ch. 6.1 - Prob. 63ESCh. 6.1 - Prob. 64ESCh. 6.1 - Egyptian Multiplication, The Rhind papyrus...Ch. 6.1 - Prob. 66ESCh. 6.1 - Prob. 67ESCh. 6.1 - Prob. 68ESCh. 6.1 - Prob. 69ESCh. 6.1 - Prob. 70ESCh. 6.1 - Prob. 71ESCh. 6.1 - Prob. 72ESCh. 6.1 - The Ionic Greek Numeration System The Ionic Greek...Ch. 6.1 - The Method of False Position The Rhind papyrus...Ch. 6.2 - Prob. 1EECh. 6.2 - Prob. 2EECh. 6.2 - Prob. 3EECh. 6.2 - Prob. 4EECh. 6.2 - Prob. 5EECh. 6.2 - Prob. 6EECh. 6.2 - Prob. 7EECh. 6.2 - Prob. 1ESCh. 6.2 - Prob. 2ESCh. 6.2 - Prob. 3ESCh. 6.2 - Write each numeral in its expanded form. 501Ch. 6.2 - Prob. 5ESCh. 6.2 - Write each numeral in its expanded form. 9045Ch. 6.2 - Prob. 7ESCh. 6.2 - Prob. 8ESCh. 6.2 - Prob. 9ESCh. 6.2 - Prob. 10ESCh. 6.2 - Prob. 11ESCh. 6.2 - Prob. 12ESCh. 6.2 - Prob. 13ESCh. 6.2 - Prob. 14ESCh. 6.2 - Prob. 15ESCh. 6.2 - Prob. 16ESCh. 6.2 - Prob. 17ESCh. 6.2 - Prob. 18ESCh. 6.2 - Use expanded forms to find each sum. 257+138Ch. 6.2 - Prob. 20ESCh. 6.2 - Use expanded forms to find each sum. 1023+1458Ch. 6.2 - Use expanded forms to find each sum. 3567+2651Ch. 6.2 - Prob. 23ESCh. 6.2 - Prob. 24ESCh. 6.2 - Prob. 25ESCh. 6.2 - Prob. 26ESCh. 6.2 - Prob. 27ESCh. 6.2 - Prob. 28ESCh. 6.2 - Prob. 29ESCh. 6.2 - Prob. 30ESCh. 6.2 - Prob. 31ESCh. 6.2 - Prob. 32ESCh. 6.2 - Write each Babylonian numeral as a Hindu-Arabic...Ch. 6.2 - Prob. 34ESCh. 6.2 - Prob. 35ESCh. 6.2 - Prob. 36ESCh. 6.2 - Prob. 37ESCh. 6.2 - Prob. 38ESCh. 6.2 - Prob. 39ESCh. 6.2 - Prob. 40ESCh. 6.2 - Prob. 41ESCh. 6.2 - Prob. 42ESCh. 6.2 - Write each Hindu-Arabic numeral as a Babylonian...Ch. 6.2 - Prob. 44ESCh. 6.2 - Prob. 45ESCh. 6.2 - Prob. 46ESCh. 6.2 - Prob. 47ESCh. 6.2 - Prob. 48ESCh. 6.2 - Prob. 49ESCh. 6.2 - Prob. 50ESCh. 6.2 - Find the sum of the Babylonian numerals. Write...Ch. 6.2 - Find the sum of the Babylonian numerals. Write...Ch. 6.2 - Prob. 53ESCh. 6.2 - Prob. 54ESCh. 6.2 - Prob. 55ESCh. 6.2 - Prob. 56ESCh. 6.2 - Prob. 57ESCh. 6.2 - Prob. 58ESCh. 6.2 - Prob. 59ESCh. 6.2 - Prob. 60ESCh. 6.2 - Prob. 61ESCh. 6.2 - Prob. 62ESCh. 6.2 - Prob. 63ESCh. 6.2 - Prob. 64ESCh. 6.2 - Prob. 65ESCh. 6.2 - Prob. 66ESCh. 6.2 - Prob. 67ESCh. 6.2 - Prob. 68ESCh. 6.2 - Prob. 69ESCh. 6.2 - Prob. 70ESCh. 6.2 - A Base Three Numeration System A student has...Ch. 6.3 - Prob. 1EECh. 6.3 - Prob. 2EECh. 6.3 - Prob. 3EECh. 6.3 - Convert the given numeral to base ten. 243fiveCh. 6.3 - Prob. 2ESCh. 6.3 - Prob. 3ESCh. 6.3 - Prob. 4ESCh. 6.3 - Prob. 5ESCh. 6.3 - Prob. 6ESCh. 6.3 - Prob. 7ESCh. 6.3 - Prob. 8ESCh. 6.3 - Prob. 9ESCh. 6.3 - Prob. 10ESCh. 6.3 - Prob. 11ESCh. 6.3 - Prob. 12ESCh. 6.3 - Prob. 13ESCh. 6.3 - Prob. 14ESCh. 6.3 - Prob. 15ESCh. 6.3 - Prob. 16ESCh. 6.3 - Prob. 17ESCh. 6.3 - Prob. 18ESCh. 6.3 - Prob. 19ESCh. 6.3 - Prob. 20ESCh. 6.3 - Prob. 21ESCh. 6.3 - Prob. 22ESCh. 6.3 - Prob. 23ESCh. 6.3 - Prob. 24ESCh. 6.3 - Prob. 25ESCh. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Prob. 27ESCh. 6.3 - Prob. 28ESCh. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Prob. 30ESCh. 6.3 - Prob. 31ESCh. 6.3 - Prob. 32ESCh. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Prob. 34ESCh. 6.3 - Prob. 35ESCh. 6.3 - Prob. 36ESCh. 6.3 - Prob. 37ESCh. 6.3 - Prob. 38ESCh. 6.3 - Prob. 39ESCh. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Prob. 41ESCh. 6.3 - Prob. 42ESCh. 6.3 - Prob. 43ESCh. 6.3 - Prob. 44ESCh. 6.3 - Prob. 45ESCh. 6.3 - Prob. 46ESCh. 6.3 - Prob. 47ESCh. 6.3 - Prob. 48ESCh. 6.3 - Prob. 49ESCh. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Prob. 52ESCh. 6.3 - Prob. 53ESCh. 6.3 - Prob. 54ESCh. 6.3 - Prob. 55ESCh. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - The Triple-Whipple-Zipple Method There is a...Ch. 6.3 - Prob. 58ESCh. 6.3 - Prob. 59ESCh. 6.3 - The Postnet Code The US. Postal Service uses a...Ch. 6.3 - Prob. 61ESCh. 6.3 - Prob. 62ESCh. 6.3 - Prob. 63ESCh. 6.3 - Prob. 64ESCh. 6.3 - Prob. 65ESCh. 6.3 - Prob. 66ESCh. 6.3 - Prob. 67ESCh. 6.3 - Prob. 68ESCh. 6.3 - Prob. 69ESCh. 6.3 - Prob. 70ESCh. 6.4 - Use the ones complement of the subtrahend and the...Ch. 6.4 - Prob. 2EECh. 6.4 - Prob. 3EECh. 6.4 - Prob. 4EECh. 6.4 - Prob. 5EECh. 6.4 - Prob. 6EECh. 6.4 - Prob. 1ESCh. 6.4 - Prob. 2ESCh. 6.4 - Prob. 3ESCh. 6.4 - Find each sum in the same base as the given...Ch. 6.4 - Prob. 5ESCh. 6.4 - Find each sum in the same base as the given...Ch. 6.4 - Find each sum in the same base as the given...Ch. 6.4 - Prob. 8ESCh. 6.4 - Prob. 9ESCh. 6.4 - Prob. 10ESCh. 6.4 - Prob. 11ESCh. 6.4 - Prob. 12ESCh. 6.4 - Prob. 13ESCh. 6.4 - Prob. 14ESCh. 6.4 - Prob. 15ESCh. 6.4 - Find each difference in the same base as the given...Ch. 6.4 - Prob. 17ESCh. 6.4 - Prob. 18ESCh. 6.4 - Prob. 19ESCh. 6.4 - Prob. 20ESCh. 6.4 - Prob. 21ESCh. 6.4 - Find each difference in the same base as the given...Ch. 6.4 - Prob. 23ESCh. 6.4 - Prob. 24ESCh. 6.4 - Prob. 25ESCh. 6.4 - Prob. 26ESCh. 6.4 - Prob. 27ESCh. 6.4 - Prob. 28ESCh. 6.4 - Prob. 29ESCh. 6.4 - Prob. 30ESCh. 6.4 - Prob. 31ESCh. 6.4 - Prob. 32ESCh. 6.4 - Prob. 33ESCh. 6.4 - Prob. 34ESCh. 6.4 - Prob. 35ESCh. 6.4 - Find each product in the same base as the given...Ch. 6.4 - Prob. 37ESCh. 6.4 - Prob. 38ESCh. 6.4 - Prob. 39ESCh. 6.4 - Prob. 40ESCh. 6.4 - Prob. 41ESCh. 6.4 - Prob. 42ESCh. 6.4 - Prob. 43ESCh. 6.4 - Prob. 44ESCh. 6.4 - Prob. 45ESCh. 6.4 - Find each quotient and remainder in the same base...Ch. 6.4 - Prob. 47ESCh. 6.4 - Prob. 48ESCh. 6.4 - Prob. 49ESCh. 6.4 - If 232x=92, find the base x.Ch. 6.4 - Prob. 51ESCh. 6.4 - Prob. 52ESCh. 6.4 - Prob. 53ESCh. 6.4 - Prob. 54ESCh. 6.4 - Prob. 55ESCh. 6.4 - Prob. 56ESCh. 6.4 - Prob. 57ESCh. 6.4 - Prob. 58ESCh. 6.4 - Prob. 59ESCh. 6.4 - A Cryptarithm In the following base four addition...Ch. 6.4 - Prob. 61ESCh. 6.4 - Prob. 62ESCh. 6.5 - Explain how you know that each of the numbers...Ch. 6.5 - Use factorials to generate the numbers in a prime...Ch. 6.5 - Use factorials and … notation to represent a...Ch. 6.5 - Prob. 1ESCh. 6.5 - Prob. 2ESCh. 6.5 - Prob. 3ESCh. 6.5 - Prob. 4ESCh. 6.5 - Prob. 5ESCh. 6.5 - Prob. 6ESCh. 6.5 - Prob. 7ESCh. 6.5 - Prob. 8ESCh. 6.5 - Prob. 9ESCh. 6.5 - Prob. 10ESCh. 6.5 - Prob. 11ESCh. 6.5 - Prob. 12ESCh. 6.5 - Prob. 13ESCh. 6.5 - Prob. 14ESCh. 6.5 - Prob. 15ESCh. 6.5 - Prob. 16ESCh. 6.5 - Prob. 17ESCh. 6.5 - Prob. 18ESCh. 6.5 - Prob. 19ESCh. 6.5 - Prob. 20ESCh. 6.5 - Prob. 21ESCh. 6.5 - Prob. 22ESCh. 6.5 - Prob. 23ESCh. 6.5 - Prob. 24ESCh. 6.5 - Prob. 25ESCh. 6.5 - Prob. 26ESCh. 6.5 - Prob. 27ESCh. 6.5 - Prob. 28ESCh. 6.5 - Prob. 29ESCh. 6.5 - Write the prime factorization of the number. 48Ch. 6.5 - Prob. 31ESCh. 6.5 - Write the prime factorization of the number. 380Ch. 6.5 - Prob. 33ESCh. 6.5 - Prob. 34ESCh. 6.5 - Prob. 35ESCh. 6.5 - Prob. 36ESCh. 6.5 - Prob. 37ESCh. 6.5 - Prob. 38ESCh. 6.5 - Prob. 39ESCh. 6.5 - Prob. 40ESCh. 6.5 - Use the sieve of Eratosthenes procedure to find...Ch. 6.5 - Prob. 42ESCh. 6.5 - Prob. 43ESCh. 6.5 - Prob. 44ESCh. 6.5 - Twin Primes Find a pair of twin primes between 300...Ch. 6.5 - Prob. 46ESCh. 6.5 - Goldbach's Conjecture In 1742, Christian Goldbach...Ch. 6.5 - Prob. 48ESCh. 6.5 - Prob. 49ESCh. 6.5 - Prob. 50ESCh. 6.5 - Prob. 51ESCh. 6.5 - Prob. 52ESCh. 6.5 - Prob. 53ESCh. 6.5 - Prob. 54ESCh. 6.5 - Prob. 55ESCh. 6.5 - Prob. 56ESCh. 6.5 - Prob. 57ESCh. 6.5 - Prob. 58ESCh. 6.5 - Prob. 59ESCh. 6.5 - Prob. 60ESCh. 6.5 - Prob. 61ESCh. 6.5 - Prob. 62ESCh. 6.5 - Prob. 63ESCh. 6.5 - Prob. 64ESCh. 6.5 - Prob. 65ESCh. 6.5 - Prob. 66ESCh. 6.5 - Prob. 67ESCh. 6.5 - Prob. 68ESCh. 6.5 - Prob. 69ESCh. 6.5 - Prob. 70ESCh. 6.5 - Prob. 71ESCh. 6.5 - Prob. 72ESCh. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 - Prob. 74ESCh. 6.5 - Prob. 75ESCh. 6.5 - Prob. 76ESCh. 6.5 - Prob. 77ESCh. 6.5 - Prob. 78ESCh. 6.5 - Prob. 79ESCh. 6.6 - Prob. 1EECh. 6.6 - Prob. 2EECh. 6.6 - Prob. 3EECh. 6.6 - Prob. 4EECh. 6.6 - Use deductive reasoning to prove that every prime...Ch. 6.6 - Prob. 6EECh. 6.6 - Prob. 1ESCh. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Prob. 4ESCh. 6.6 - Prob. 5ESCh. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Prob. 8ESCh. 6.6 - Prob. 9ESCh. 6.6 - Prob. 10ESCh. 6.6 - Prob. 11ESCh. 6.6 - Prob. 12ESCh. 6.6 - Prob. 13ESCh. 6.6 - Prob. 14ESCh. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Prob. 16ESCh. 6.6 - Prob. 17ESCh. 6.6 - Prob. 18ESCh. 6.6 - Prob. 19ESCh. 6.6 - Prob. 20ESCh. 6.6 - In 1876, Édouard Lucas proved, without the aid of...Ch. 6.6 - Prob. 22ESCh. 6.6 - Prob. 23ESCh. 6.6 - Prob. 24ESCh. 6.6 - Prob. 25ESCh. 6.6 - Prob. 26ESCh. 6.6 - Prob. 27ESCh. 6.6 - Prob. 28ESCh. 6.6 - Prob. 29ESCh. 6.6 - Prob. 30ESCh. 6.6 - Prob. 31ESCh. 6.6 - Prob. 32ESCh. 6.6 - Prob. 33ESCh. 6.6 - Prob. 34ESCh. 6.6 - Prob. 35ESCh. 6.6 - Amicable Numbers The Greeks considered the pair of...Ch. 6.6 - Prob. 37ESCh. 6.6 - Prob. 38ESCh. 6.6 - Prob. 39ESCh. 6.6 - Prob. 40ESCh. 6.6 - Fermat Numbers Numbers of the form 22n+1, where n...Ch. 6.6 - Prob. 42ESCh. 6.6 - Weird Numbers Any number that is an abundant...Ch. 6.6 - Prob. 44ESCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Write each Hindu-Arabic numeral in expanded form....Ch. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Write each Babylonian numeral as a Hindu-Arabic...Ch. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Write each Hindu-Arabic numeral as Mayan numeral....Ch. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Prob. 74RECh. 6 - Prob. 75RECh. 6 - Prob. 76RECh. 6 - Prob. 77RECh. 6 - Prob. 78RECh. 6 - Prob. 79RECh. 6 - Prob. 80RECh. 6 - Prob. 81RECh. 6 - Prob. 82RECh. 6 - Prob. 83RECh. 6 - Prob. 84RECh. 6 - Prob. 85RECh. 6 - Prob. 86RECh. 6 - Prob. 87RECh. 6 - Prob. 88RECh. 6 - Write 3124 using Egyptian hieroglyphics.Ch. 6 - Prob. 2TCh. 6 - Write the Roman numeral MCDXLVII as a Hindu-Arabic...Ch. 6 - Prob. 4TCh. 6 - Write 67,485 in expanded form.Ch. 6 - Prob. 6TCh. 6 - Write the Babylonian numeral as a Hindu-Arabic...Ch. 6 - Write 9675 as a Babylonian numeral.Ch. 6 - Write the Mayan numeral as a Hindu-Arabic numeral.Ch. 6 - Write 502 as a Mayan numeral.Ch. 6 - Convert 3542six to base ten.Ch. 6 - Convert 2148 to a. base eight and b. base twelve.Ch. 6 - Prob. 13TCh. 6 - Prob. 14TCh. 6 - Prob. 15TCh. 6 - Prob. 16TCh. 6 - Prob. 17TCh. 6 - Prob. 18TCh. 6 - Prob. 19TCh. 6 - Determine whether 1001 is a prime number or a...Ch. 6 - Use divisibility tests to determine whether...Ch. 6 - Use divisibility test to determine whether...Ch. 6 - Prob. 23TCh. 6 - Prob. 24TCh. 6 - Prob. 25T
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