C++ How to Program (10th Edition)
C++ How to Program (10th Edition)
10th Edition
ISBN: 9780134448237
Author: Paul J. Deitel, Harvey Deitel
Publisher: PEARSON
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Chapter 15, Problem 15.24E

(Sieve of Eratosthenes) Modify Exercise 15.23, the Sieve of Eratosthenes, so that, if the number the user inputs into the program is not prime, the program displays the prime factors of the number. Remember that a prime number’s factors are only 1 and the prime number itself. Even- nonprime number has a unique prime factorization. For example, the factors of 54 are 2, 3, 3 and 3. When these values are multiplied together, the result is 54. For the number 54, the prime factors output should be 2 and 3.

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(GREATEST COMMON DIVISOR) The greatest common divisor of integers x and y is the largest integer that evenly divides into both x and y. Write and test a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows: If y is equal to 0, then gcd (x, y) is x; otherwise, gcd (x, y) is gcd (y, x % y), where % is the remainder operator.
Q2) (Perfect Numbers) An integer number is said to be a perfect number if its factors, including 1 (but not the number itself), sum to the number. For example, 6 is a perfect number because 6 = 1 + 2 + 3. Write a function perfect that determines if parameter number is a perfect number. Use this function in a program that determines and prints all the perfect numbers between 1 and 1000. Print the factors of each perfect number to confirm that the number is indeed perfect. Challenge the power of your computer by testing numbers much larger than 1000.
(True or False) Seven different positive integers are randomly chosen between 1 and 2022 (including 1 and 2022).There must be a pair of these integers has a difference that is a multiple of 6.
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