Problem 1E: Determine whether each of the following statements is true: 8 divides 56. Problem 2E: Determine whether each of the following statements is true: 21 is a multiple of 2. Problem 3E: Determine whether each of the following statements is true: 27 is a multiple of 6. Problem 4E: Determine whether each of the following statements is true: 5 is a divisor of 35. Problem 5E: Determine whether each of the following statements is true: 9 is a factor of 96. Problem 6E: Determine whether each of the following statements is true: 14 divides 42. Problem 7E: Determine whether each of the following statements is true: 7 is a divisor of 63. Problem 8E: Determine whether each of the following statements is true: 6 is a factor of 76. Problem 9E: Check each of the following numbers for divisibility by each of these numbers: 2, 3, 4, 5, 6, 8, 9,... Problem 10E: Check each of the following numbers for divisibility by each of these numbers: 2, 3, 4, 5, 6, 8, 9,... Problem 11E: Check each of the following numbers for divisibility by each of these numbers: 2, 3, 4, 5, 6, 8, 9,... Problem 12E: Check each of the following numbers for divisibility by each of these numbers: 2, 3, 4, 5, 6, 8, 9,... Problem 13E: In Exercises 1316, find all values for d that make the indicated divisibility test successful.... Problem 14E: In Exercises 1316, find all values for d that make the indicated divisibility test successful.... Problem 15E: In Exercises 1316, find all values for d that make the indicated divisibility test successful.... Problem 16E: In Exercises 1316, find all values for d that make the indicated divisibility test successful.... Problem 17E: In Exercises 1720, use a calculator to determine if the first number divides the second. 447 and 17,... Problem 18E Problem 19E Problem 20E Problem 21E: Provide a counterexample to show that each of the following statements is false: If 2 and 4 divide... Problem 22E: Provide a counterexample to show that each of the following statements is false: If 3 and 6 divide... Problem 23E: Provide a counterexample to show that each of the following statements is false: If 10 and 4 divide... Problem 24E: Provide a counterexample to show that each of the following statements is false: If 4 and 6 divide... Problem 25E: What is the largest prime divisor you must try as a divisor of the given number n before you know... Problem 26E: What is the largest prime divisor you must try as a divisor of the given number n before you know... Problem 27E: What is the largest prime divisor you must try as a divisor of the given number n before you know... Problem 28E: What is the largest prime divisor you must try as a divisor of the given number n before you know... Problem 29E: Use the Sieve of Eratosthenes to find all prime numbers between 51 and 100, inclusive. Problem 30E: Use the Sieve of Eratosthenes to find all prime numbers between 101 and 120, inclusive. Problem 31E: Factor each of the following natural numbers. If the number is prime, state so. 231 Problem 32E: Factor each of the following natural numbers. If the number is prime, state so. 89 Problem 33E Problem 34E Problem 35E Problem 36E: Factor each of the following natural numbers. If the number is prime, state so. 143 Problem 37E Problem 38E Problem 39E Problem 40E: Factor each of the following natural numbers. If the number is prime, state so. 396 Problem 41E Problem 42E Problem 43E Problem 44E: Factor each of the following natural numbers. If the number is prime, state so. 403 Problem 45E Problem 46E Problem 47E Problem 48E: Use prime factorization to find the GCD and LCM of each of the following pairs of natural numbers:... Problem 49E Problem 50E Problem 51E: Use prime factorization to find the GCD and LCM of each of the following pairs of natural numbers:... Problem 52E: Use prime factorization to find the GCD and LCM of each of the following pairs of natural numbers:... Problem 53E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 54E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 55E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 56E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 57E Problem 58E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 59E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 60E: In Exercises 5360, a use the Euclidean algorithm to find the GCD of the two numbers; then b use your... Problem 61E: You can find the GCD of three numbers a, b, and c by first finding GCDa, b, call it d, and then... Problem 62E: You can find the GCD of three numbers a, b, and c by first finding GCDa, b, call it d, and then... Problem 63E: You can find the GCD of three numbers a, b, and c by first finding GCDa, b, call it d, and then... Problem 64E: You can find the GCD of three numbers a, b, and c by first finding GCDa, b, call it d, and then... Problem 65E: Stacking iPad covers. A college bookstore manager has 24 plain and 16 leather iPad covers. If she... Problem 66E: Packaging sports cards. A sports card dealer has 54 baseball cards and 72 football cards. He wishes... Problem 67E: Servicing a car Your new vintage 1965 Corvette convertible requires an oil change every 2, 500 miles... Problem 68E: Training for a race. In training for a half-marathon, you and your friend Mike are running around a... Problem 69E Problem 70E: Scheduling nurses shifts. Carla and Laverne are nurses who occasionally work in the emergency room.... Problem 71E: Storing medical supplies. In a medical supply room, there are 36 packages of type O positive blood... Problem 72E: 73. Displaying store merchandise. A sporting goods store has 20 instructional DVDs on skiing and 12... Problem 73E Problem 74E: Scheduling lawn service. At the Berkshire Country Club, the lawn service cuts the grass every 8 days... Problem 75E: Monitoring pollution. The Environmental Protection Agency is monitoring the Lackawanna River to... Problem 76E: Movie showings. At the 24/7 classic Movie Plex, Gone with the Wind shows every 120 minutes,... Problem 77E: If you were using the Sieve of Eratosthenes to find the primes up to 300, what is the largest prime... Problem 78E: Explain why the divisibility test for 4 works by considering the number 36, 824. It helps to think... Problem 79E: Explain why the divisibility test for 3 works by considering the number 5, 712. It helps to think of... Problem 80E: Do a number of examples of finding the GCD and LCM of two numbers first using the prime... Problem 81E: In addition to avoiding their predators, another advantage of the 13- and 17-year emergence pattern... Problem 82E: Cicadas. Continuing the discussion in Exercise 81, suppose that a predator of both type A and type B... Problem 83E: In Exercises 83 and 84, assume that type A cicada has a 10-year cycle and type B cicada has a... Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E: Sophie Germain primes. List the first 10 Sophie Germain primes. Problem 90E: Sophie Germain primes. Determine whether or not the following primes are Sophie Germain primes: a.... Problem 91E: Mersenne primes. a. Find the first five Mersenne primes. b. Give an example of a prime p such that... Problem 92E: Mersenne primes. As of February 2016, the largest known Mersenne prime was 274, 207, 2811, which we... Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E format_list_bulleted