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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 6.5, Problem 70ES

Textbook Problem

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** 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

Determine the number of divisors of each composite number.

84

To determine

**To calculate:**

To determine the number of divisors of composite number 84

**Given information:**

Composite number 84 is given

**Calculation:**

Consider the number 84

The prime factorization of 84 is

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B5sixteenCh. 6.3 - Convert the given numeral to base ten. 4AtwelveCh. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Convert the given base ten numeral to the...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use expanded forms to convert the given base two...Ch. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Use the double-dabble method to convert the given...Ch. 6.3 - Convert given numeral to the indicated base. 34six...Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert given numeral to the indicated base....Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - Convert the given numeral directly (without first...Ch. 6.3 - The Triple-Whipple-Zipple Method There is a...Ch. 6.3 - Determine whether the following statements are...Ch. 6.3 - The ASCII Code ASCII, pronounced ask-key, is an...Ch. 6.3 - The Postnet Code The US. 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Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - Every prime number has a divisibility test. Many...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - A divisibility test for 13 To determine whether a...Ch. 6.5 - Factorial Primes A prime number of the form. n!1....Ch. 6.5 -
Ch. 6.5 - A Divisibility Test for 17 Determine a...Ch. 6.5 - A Divisibility Test for 19 Determine a...Ch. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 - Number of Divisors of a Composite Number The...Ch. 6.5 -
Ch. 6.5 -
Ch. 6.5 -
Ch. 6.5 - The RSA Algorithm In 1977, Ron Rivest, Adi Shamir,...Ch. 6.5 -
Ch. 6.6 - Use the above technique to find the Sum of the...Ch. 6.6 - Use the above technique to find the Sum of the...Ch. 6.6 - Use the above technique to find the Sum of the...Ch. 6.6 - Use the above technique to find the Sum of the...Ch. 6.6 - Use deductive reasoning to prove that every prime...Ch. 6.6 - Use inductive reasoning to decide whether every...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each number is perfect,...Ch. 6.6 - Determine whether each Mersenne number is a prime...Ch. 6.6 - Determine whether each Mersenne number is a prime...Ch. 6.6 - Determine whether each Mersenne number is a prime...Ch. 6.6 - Determine whether each Mersenne number is a prime...Ch. 6.6 - In 1876, Ă‰douard Lucas proved, without the aid of...Ch. 6.6 - In 1952, Raphael M. Robinson proved, with the aid...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Determine the number of digits in the given...Ch. 6.6 - Verify that x=9,y=15, and n=5 do not yield a...Ch. 6.6 - Verify that x=7,y=19, and n=6 do not yield a...Ch. 6.6 - Determine whether each of the following statements...Ch. 6.6 - Show that 4078n+3433n=12,406n cannot be a solution...Ch. 6.6 - Fermat's Little Theorem A theorem known as...Ch. 6.6 - Amicable Numbers The Greeks considered the pair of...Ch. 6.6 - A Sum of Cubes Property The perfect number 28 can...Ch. 6.6 - A Sum of the Digits Theorem If you sum the digits...Ch. 6.6 - A Sum of Reciprocals Theorem The sum of the...Ch. 6.6 - The Smallest Odd Abundant Number Determine the...Ch. 6.6 - Fermat Numbers Numbers of the form 22n+1, where n...Ch. 6.6 - Semiperfect Numbers Any number that is the sum of...Ch. 6.6 - Weird Numbers Any number that is an abundant...Ch. 6.6 - A False Prediction In 1811, Peter Barlow wrote in...Ch. 6 - Write 4,506,325 using Egyptian hieroglyphics.Ch. 6 - Write 3,124,043 using Egyptian hieroglyphics.Ch. 6 - Write the Egyptian hieroglyphic as a Hindu-Arabic...Ch. 6 - Write the Egyptian hieroglyphic as a Hindu-Arabic...Ch. 6 - Write each Roman numeral as a Hindu-Arabic...Ch. 6 - Write each Roman numeral as a Hindu-Arabic...Ch. 6 - Write each Roman numeral as a Hindu-Arabic...Ch. 6 - Write each Roman numeral as a Hindu-Arabic...Ch. 6 - Write each Hindu-Arabic numeral as a Roman...Ch. 6 - Write each Hindu-Arabic numeral as a Roman...Ch. 6 - Write each Hindu-Arabic numeral as a Roman...Ch. 6 - Write each Hindu-Arabic numeral as a Roman...Ch. 6 - Write each Hindu-Arabic numeral in expanded form....Ch. 6 - Write each Hindu-Arabic numeral in expanded form....Ch. 6 - Simplify each expanded form....Ch. 6 - Simplify each expanded form....Ch. 6 - Write each Babylonian numeral as a Hindu-Arabic...Ch. 6 - Write each Babylonian numeral as a Hindu-Arabic...Ch. 6 - Write each Babylonian numeral as a Hindu-Arabic...Ch. 6 - Write each Babylonian numeral as a Hindu-Arabic...Ch. 6 - Write each Hindu-Arabic numeral as Baylonian...Ch. 6 - Write each Hindu-Arabic numeral as Baylonian...Ch. 6 - Write each Hindu-Arabic numeral as Baylonian...Ch. 6 - Write each Hindu-Arabic numeral as Baylonian...Ch. 6 - Write each Mayan numeral as a Hindu-Arabic...Ch. 6 - Write each Mayan numeral as a Hindu-Arabic...Ch. 6 - Write each Mayan numeral as a Hindu-Arabic...Ch. 6 - Write each Mayan numeral as a Hindu-Arabic...Ch. 6 - Write each Hindu-Arabic numeral as Mayan numeral....Ch. 6 - Write each Hindu-Arabic numeral as Mayan numeral....Ch. 6 - Write each Hindu-Arabic numeral as Mayan numeral....Ch. 6 - Write each Hindu-Arabic numeral as Mayan numeral....Ch. 6 - Convert each numeral to base ten. 45sixCh. 6 - Convert each numeral to base ten. 172nineCh. 6 - Convert each numeral to base ten. E3sixteenCh. 6 - Convert each numeral to base ten. 1BAtwelveCh. 6 - Convert each base ten numeral to the indicated...Ch. 6 - Convert each base ten numeral to the indicated...Ch. 6 - Convert each base ten numeral to the indicated...Ch. 6 - Convert each base ten numeral to the indicated...Ch. 6 - Convert each numeral to the indicated base....Ch. 6 - Convert each numeral to the indicated base....Ch. 6 - Convert each numeral to the indicated base....Ch. 6 - Convert each numeral to the indicated base....Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Convert each numeral directly (without first...Ch. 6 - Use the double-dabble method to convert each base...Ch. 6 - Use the double-dabble method to convert each base...Ch. 6 - Use the double-dabble method to convert each base...Ch. 6 - Use the double-dabble method to convert each base...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Perform the indicated operation. Write the answers...Ch. 6 - Use divisibility tests to determine whether the...Ch. 6 - Use divisibility tests to determine whether the...Ch. 6 - Determine whether the given number is a prime...Ch. 6 - Determine whether the given number is a prime...Ch. 6 - Determine whether the given number is a prime...Ch. 6 - Determine whether the given number is a prime...Ch. 6 - Determine the prime factorization of the given...Ch. 6 - Determine the prime factorization of the given...Ch. 6 - Determine the prime factorization of the given...Ch. 6 - Determine the prime factorization of the given...Ch. 6 - Determine whether the given number is perfect,...Ch. 6 - Determine whether the given number is perfect,...Ch. 6 - Determine whether the given number is perfect,...Ch. 6 - Determine whether the given number is perfect,...Ch. 6 - Use Euclid's perfect number-generating procedure...Ch. 6 - Use Euclid's perfect number-generating procedure...Ch. 6 - Use the Egyptian doubling procedure to find the...Ch. 6 - Use the Egyptian doubling procedure to find the...Ch. 6 - Use the Egyptian doubling procedure to find the...Ch. 6 - Use the Egyptian doubling procedure to find the...Ch. 6 - Find the number of digits in the Mersenne number...Ch. 6 - Find the number of digits in the Mersenne number...Ch. 6 - How many Odd perfect numbers had been discovered...Ch. 6 - Determine whether there is a natural number z such...Ch. 6 - Write 3124 using Egyptian hieroglyphics.Ch. 6 - Write the Egyptian hieroglyphic as a Hindu-Arabic...Ch. 6 - Write the Roman numeral MCDXLVII as a Hindu-Arabic...Ch. 6 - Write 2609 as Roman numeral.Ch. 6 - Write 67,485 in expanded form.Ch. 6 - Simplify: (5105)+(3104)+(2102)+(8101)+(4100)Ch. 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 - Convert 4567eight to binary form.Ch. 6 - Convert 101010110111two to hexadecimal form.Ch. 6 - Perform the indicated operation. Write the answer...Ch. 6 - Perform the indicated operation. Write the answer...Ch. 6 - Perform the indicated operation. Write the answer...Ch. 6 - Perform the indicated operation. Write the answer...Ch. 6 - Determine the prime factorization of 230.Ch. 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 - Determine whether 96 is perfect, deficient, or...Ch. 6 - Use Euclid's perfect number generating procedure...Ch. 6 - Explain how you know (without doing any...

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