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Mathematical Excursions (MindTap Course List)4th Edition
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Every prime number has a divisibility test. Many of these divisibility tests are slight variations of the following divisibility test for 7. A divisibility test for 7 To determine whether a given base ten number is divisible by 7, double the ones digit of the given number. Find the difference between this number and the number formed by omitting the ones digit from the given number. If necessary, repeat this procedure until you obtain a small final difference. If the final difference is divisible by 7, then the given number is also divisible by 7. If the final difference is not divisible by 7, then the given number is not divisible by 7. Example Use the above divisibility test to determine whether 301 is divisible by 7. Solution The double of the ones digit is 2. Subtracting 2 from 30, which is the number formed by omitting the ones digit from the original number, yields 28. Because 28 is divisible by 7, the original number 301 is divisible by 7. Use the divisibility test for 7, given above, to determine whether each number is divisible by 7. 204,316

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 6.5, Problem 55ES
Textbook Problem
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Every prime number has a divisibility test. Many of these divisibility tests are slight variations of the following divisibility test for 7.

A divisibility test for 7 To determine whether a given base ten number is divisible by 7, double the ones digit of the given number. Find the difference between this number and the number formed by omitting the ones digit from the given number. If necessary, repeat this procedure until you obtain a small final difference.

If the final difference is divisible by 7, then the given number is also divisible by 7.

If the final difference is not divisible by 7, then the given number is not divisible by 7.

Example Use the above divisibility test to determine whether 301 is divisible by 7.

Solution The double of the ones digit is 2. Subtracting 2 from 30, which is the number formed by omitting the ones digit from the original number, yields 28. Because 28 is divisible by 7, the original number 301 is divisible by 7.

Use the divisibility test for 7, given above, to determine whether each number is divisible by 7.

204,316

To determine

To calculate:

To determine whether 204,316 is divisible by 7

Explanation of Solution

Given information:

Number 204,316 is given for divisibility test for 7

Calculation:

Consider the number 204,316.

The ones digit is 6, so double of 6 is 12.

Subtract 12 from 204,31 gives 20419.

Now, the ones digit in 20419 is 9.

The double of 9 is 18...

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Mathematical Excursions (MindTap Course List)
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In base...Ch. 6.4 - Explain why there is no numeration system with a...Ch. 6.4 - A Cryptarithm In the following base four addition...Ch. 6.4 - A Cryptarithm In the following base Six addition...Ch. 6.4 - Negative Base Numerals It is possible to use a...Ch. 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 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine all natural number divisors of the given...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Determine whether each number is a prime number or...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Use the divisibility tests in Table 6.13 to...Ch. 6.5 - Write the prime factorization of the number. 18Ch. 6.5 - Write the prime factorization of the number. 48Ch. 6.5 - Write the prime factorization of the number. 120Ch. 6.5 - Write the prime factorization of the number. 380Ch. 6.5 - Write the prime factorization of the number. 425Ch. 6.5 - Write the prime factorization of the number. 625Ch. 6.5 - Write the prime factorization of the number. 1024Ch. 6.5 - Write the prime factorization of the number. 1410Ch. 6.5 - Write the prime factorization of the number. 6312Ch. 6.5 - Write the prime factorization of the number. 3155Ch. 6.5 - Write the prime factorization of the number....Ch. 6.5 - Write the prime factorization of the number....Ch. 6.5 - Use the sieve of Eratosthenes procedure to find...Ch. 6.5 - Use your list of prime numbers from Exercise 41 to...Ch. 6.5 - Twin Primes If the natural numbers n and n+2 are...Ch. 6.5 - Twin Primes Find a pair of twin primes between 200...Ch. 6.5 - Twin Primes Find a pair of twin primes between 300...Ch. 6.5 - A Prime Triplet If the natural numbers n, n+2, and...Ch. 6.5 - Goldbach's Conjecture In 1742, Christian Goldbach...Ch. 6.5 - Perfect Squares The square of a natural number is...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 - 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, Édouard 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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