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Mathematical Excursions (MindTap Course List)4th Edition
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Use divisibility tests to determine whether the given numbers is divisible by 2, 3, 4, 5, 6, 8, 9, 10, or 11. 4268

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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, Problem 66RE
Textbook Problem
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Use divisibility tests to determine whether the given numbers is divisible by 2, 3, 4, 5, 6, 8, 9, 10, or 11.

4268

To determine

Use the divisibility test to find out if the below number is divisible by 2,3,4,5,6,8,9,10or11

4268

Explanation of Solution

Given:

The number as 4268

Formula Used:

Divisibility rules as follows:

  1. Divisibility by 2 : The number is divisible by 2 only when the number is even
  2. Divisibility by 3 : The number is divisible by 3 only when the sum of the digits of the number is divisible by 3
  3. Divisibility by 4 : The number is divisible by 4 when the last two digits of number is divisible by 4
  4. Divisibility by 5 : The number is divisible by 5 when the last digit of the number is either 5 or 0
  5. Divisibility by 6 : The number is divisible by 6 only when the number is divisible by both 2 and 3
  6. Divisibility by 8 : The number is divisible by 8 when the last three digits of number is divisible by 8
  7. Divisibility by 9 : The number is divisible by 9 only when the sum of the digits of the number is divisible by 9
  8. Divisibility by 10 : The number is divisible by 10 when the last digit of the number is 0
  9. Divisibility by 11 : Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.

Calculation:

Given the below number

4268

Divisibility by2

Since, 4268 is even, hence the number is divisible by 2

Divisibility by3:

Since, sum of digits =4+2+6+8=20

Also, 20 is not divisible by 3

Thus, 4268 is not divisible by 3

Divisibility by4:

Last two digits of number =68

Also, 68 is divisible by 4

Thus, 4268 is divisible by 4

Divisibility by5

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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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